# Chapter 4. Cartel deterrence and the labour market for managers

This chapter examines the impact of different antitrust regimes on deterring cartel behaviour. It presents the results of a laboratory experiment that sheds light on how competing regulatory frameworks may affect managers’ incentives to collude and, in turn, managers’ labour markets.

## Introduction

Although they share a similar underlying rationale, the United States (US) and the European Union (EU) antitrust regimes differ in several particular areas. One such area is the punishment of cartels, possibly the most worrisome competition law infringement (OECD, 2005).

The U.S. Department of Justice (DOJ hereafter) pursues individual convictions of both civil/administrative and criminal nature along with corporate fines since the inception of the Sherman Act (1890): “[v]iolations are punishable by fines and imprisonment”.

Within the EU, Article 23 of Council Regulation (EC) No. 1 of 16 December 2002 introduces the legal basis for implementing fines in case of violations: “2. The Commission may by decision impose fines on undertakings and associations of undertakings where, either intentionally or negligently: (a) they infringe Article 81 or Article 82 of the Treaty; […] 5. Decisions […] shall not be of a criminal law nature”. Additionally, until relatively recently, EU jurisdictions typically only applied corporate fines. The United Kingdom (UK) and an increasing number of EU countries (Austria, Belgium, Denmark, Estonia, France, Germany, Greece, Hungary, Ireland, Italy, Poland, Portugal, Romania, the Slovak Republic, Slovenia and Spain) now also include in their jurisdictions the possibility of individual penal sanctions for cartels.

The goal of this chapter is to provide experimental evidence on the relative effectiveness of individual fines vs. corporate fines to deter cartels. This is somewhat related to two different antitrust frameworks: the US antitrust framework, which applies individual fines; and the EU antitrust framework, which is mainly based on corporate fines. The issue at stake has clear implications for competition policy and can be of interest to academic economists as well as competition authorities and antitrust practitioners.

In addition, we analyse the extent to which such antitrust regimes may influence the labour market for managers, not only through the type of contract they are offered – fixed salary vs. fixed salary plus a variable component – but also through salary levels. To the best of our knowledge, this type of analysis – the relationship between antitrust regimes and manager labour markets – is novel in the literature.

More specifically, our research goals are:

• Do antitrust law regimes involving individual fines have larger cartel deterrence power than antitrust regimes encompassing only corporate fines?

• Do antitrust regimes cause distortions in managers’ labour market, namely by making particular types of contracts more appealing to shareholders?

Our research paper is theoretical and experimental. The theoretical model looks into the incentives for Bertrand oligopolists to form cartels. Each firm is operated by a manager, whose contract (offered by the principal-shareholders) is a combination of a fixed and a variable salary component that depends on the firm’s revenue. As usual, within a principal-agent framework, managers choose whether or not to accept the contract and, in case they do accept, in addition to setting prices, managers can choose to form an explicit cartel, thus sustaining monopoly prices. As outlined above, we look at manager incentives for collusion under two antitrust regimes – one where, if the cartel is detected, fines are revenue-based and are levied on the firm (corporate fines); and another where fines are salary-based and levied on the manager (individual fines).

Our underlying rationale for following an experimental approach as a complement to our theoretical approach is the following. It is well known and well acknowledged that the empirical literature in the broad field of economics of cartels suffers from sample selection bias. The main reason is that observed empirical data consists of detected cartels, which may not be representative of the whole population of cartels (and which includes those that have not been detected).

In addition, empirical work usually suffers from the inability of measuring all the possible factors that may affect an outcome or variable of interest. As well explained in Chamberlain (1948), “[t]he data of real life are necessarily the product of many influences other than those which it is desired to isolate [...] [u]nwanted variables cannot be held constant or eliminated…”. By contrast, the toolkit of experimental economics allows us to prevent the limitations inherent to empirical work. Indeed, experiments allow us “to study in isolation and under known conditions the effects of particular forces” (Ruffle and Normann, 2011). In contrast to empirical work, laboratory experiments generate data under controlled conditions, which, by changing the experimental conditions and environment, allow us to make meaningful comparisons. In other words, the researcher has the possibility of changing just one variable of interest in each treatment of the experiment, maintaining all else equal. This methodology more adequately reveals any nexus of causality between variables, whereas with empirical data, more often than not, we cannot unambiguously uncover causal relationships.

Naturally, experiments also have disadvantages, especially those in the industrial organisation field: subjects are typically students, who play the role of a fictitious economic agent (usually firms), in a highly stylised economic environment with fairly low stakes (and usually with no downside, as subjects do not typically lose money in an experiment). Nevertheless, many of the criticisms usually made to the application of experiments in industrial organisations are not fully convincing or, at least in some cases, can be easily dismantled (Ruffle and Normann, 2011; Hinloopen and Normann, 2011).

The experimental part of the research paper involves quadropoly (four firms) markets, where identical firms selling a homogenous product play a repeated Bertrand game with inelastic demand. We choose experimental markets with four firms since there is experimental evidence of greater gains and higher incentives from cartel behaviour in such markets (Fonseca and Normann, 2012; 2014).

Our main experiment consists of four treatments:

• A baseline treatment where subjects cannot communicate (“NoChat”).

• A treatment where subjects can communicate and choose whether or not to form a cartel, without the presence of a competition authority (“ChatNoLaw”).

• A treatment where subjects can communicate and the competition authority levies individual fines on firms’ managers if a cartel is detected (“ChatUS”).

• A treatment where subjects can communicate but only corporate fines are levied in case of cartel detection (“ChatEU”).

Each treatment is made up of 12 sessions of 12 subjects each, which are divided into 2 sets of 6 sessions (which we refer to as Phase 1 and Phase 2). Subjects in the first set of 6 sessions (Phase 1) play the role of firm owners and choose contracts for their managers in the second set of 6 sessions (Phase 2). In the second set of sessions, subjects play the role of managers in four different markets, where in each market they are randomly matched with three other subjects from the same session. In a market, managers are expected to make a pricing decision per period, until the market eventually ends (more details below).

In each market, managers are offered a particular salary by their firm owner. The salary has a fixed component and a revenue-based component. A contract can be “low-powered” or “high-powered”. Both types of contract have the same fixed component, but high-powered contracts have a larger revenue-based component than low-powered contracts. Each subject makes decisions in two markets under a high-powered contract and in the other two markets under a low-powered contract.

In the baseline treatment (NoChat), subjects make their pricing decisions in each market in the absence of any communication. By contrast, in the other three treatments, subjects have the choice of whether to start communicating via a chat messenger. As a result, we endogenise cartel formation as in Fonseca and Normann (2014). Endogenising cartel formation allows us to study cartel deterrence, which is one of the goals of the paper.

In our first treatment, ChatNoLaw, cartel formation has no negative consequences to participants: no competition law exists and cartels, if formed, attract no sanctions whatsoever. By contrast, competition law is assumed to exist in the ChatUS and ChatEU treatments and an antitrust authority monitoring each market may punish cartels if they are detected. We follow Fonseca and Normann (2014) and various experiments on leniency programmes (e.g. Apesteguia et al., 2007; Hinloopen and Soetevent, 2008; Bigoni et al., 2012) and assume that, with a fixed probability, the competition authority may audit a market. If a market is audited and managers in that market have decided to communicate, the cartel is automatically detected and the authority will levy a punishment that differs depending on the applicable antitrust regime.

In the ChatUS treatment, this punishment is individual in nature and is assumed to take the form of an individual fine that falls on the manager’s salary. Under an antitrust regime with individual convictions, offenders could face jail time, but we are, for obvious reasons, unable to implement such a punishment in an experiment. Therefore, we make the assumption that individual punishments in such antitrust regimes can be made equivalent to a monetary reduction in the manager’s salary. By contrast, in the ChatEU treatment, the punishment takes the form of a corporate fine, i.e. there is a reduction in firms’ revenues (and only indirectly, through the variable salary component, managers’ salaries).

In a nutshell, our results are the following. From a theoretical viewpoint, we find that particular type of fine for collusion does play an important role in managers’ decisions. Shareholders, anticipating managers’ choices, find it optimal to offer fixed wage salaries in a corporate fine antitrust regime, but when fines are of an individual nature, they choose instead a combination of a fixed and a variable component or, in some cases, a purely variable contract.

From an experimental viewpoint, our main conclusion is that, while both type of fines have some success in deterring collusion, the observed behaviour diverges significantly from the theoretical expectation. One possible explanation for this divergence is (unobserved) manager heterogeneity: not only may managers be different from one another (e.g. in their degree of risk aversion), but they may also diverge from one another in terms of strategy choices, e.g. strategies played under competition or strategies played in case of deviation from the cartel agreement.

Not only do the questions we address in this research project have academic relevance, but they also have implications for competition policy. In fact, a recent ongoing debate has evolved on the criminalisation of EU competition policy (Shaffer et al., 2015). In addition, Shaffer et al. (2015) point out that there is a worldwide trend in adding a criminal law component to competition policy. For example, among BRICS (Brazil, Russia, India, China and South Africa) countries, Brazil and South Africa have started to introduce individual sanctions (fines and imprisonment) for cartel offences; also, a growing number of Latin American and Asian countries have been doing so. We hope to be able to contribute to this ongoing discussion with the outputs of this research paper.

## Context and problem-setting

In this subsection, we give an overview of the European Union – France, Germany and the United Kingdom (UK), the top three European countries in gross domestic product (GDP) terms – Canada and the United States legal frameworks for dealing with cartels. This overview reveals the contrast between the EU and the US in punishing detected cartels. France, Germany and the UK stand closer to the US regime; in fact, these countries have a cartel enforcement regime within which managers and executives may be punished through monetary fines and/or imprisonment. Nevertheless, Canada and the United States tend to have, in their jurisdictions, higher maximum individual punishments than these three European countries.

### EU legislation

The legal framework within which the European Commission (EC), through the Directorate-General for Competition (DG Competition), fights cartels is provided by Article 101 of the Treaty on the Functioning of the European Union (TFEU, Box 4.1).

Box ‎4.1. Treaty on the Functioning of the European Union, Section 101

“1. The following shall be prohibited as incompatible with the internal market: all agreements between undertakings, decisions by associations of undertakings and concerted practices which may affect trade between Member States and which have as their object or effect the prevention, restriction or distortion of competition within the internal market, and in particular those which:

• directly or indirectly fix purchase or selling prices or any other trading conditions

• limit or control production, markets, technical development, or investment

• share markets or sources of supply

• apply dissimilar conditions to equivalent transactions with other trading parties, thereby placing them at a competitive disadvantage

• make the conclusion of contracts subject to acceptance by the other parties of supplementary obligations which, by their nature or according to commercial usage, have no connection with the subject of such contracts.

2. Any agreements or decisions prohibited pursuant to this Article shall be automatically void.

3. The provisions of paragraph 1 may, however, be declared inapplicable in the case of:

• any agreement or category of agreements between undertakings, – any decision or category of decisions by associations of undertakings

• any concerted practice or category of concerted practices, which contributes to improving the production or distribution of goods or to promoting technical or economic progress, while allowing consumers a fair share of the resulting benefit, and which does not:

• impose on the undertakings concerned restrictions, which are not indispensable to the attainment of these objectives

• afford such undertakings the possibility of eliminating competition in respect of a substantial part of the products in question.”

Source: European Union (2012), Consolidated Version of the Treaty on the Functioning of the European Unionhttps://eur-lex.europa.eu/legal-content/EN/TXT/?uri=celex%3A12012E%2FTXT (accessed on 21 March 2019).

The first paragraph of Article 101 of the TFEU prohibits all agreements between competitors that prevent, restrict or distort competition within the EU and that may adversely affect trade between member states. In addition, Article 101 also lists a series of agreements between firms that, if put into place, will be automatically declared legally invalid. Finally, Paragraph 3 of Article 101 provides exceptions, whereby agreements that would normally be declared null are instead considered legally valid if they bring about efficiency gains due to innovation (improved production, distribution of products or promotion of technical or economic progress) and do not impose unnecessary restrictions or significantly restrict competition.

Discussing the method for computing fines set out by EU competition law is beyond the scope of this paper (see European Commission, 2013). However, the essence of our theoretical and experimental approaches involves the distinction between corporate fines (with no criminalisation), as under the EU framework,1 and punishment mechanisms targeting both firms and individuals (criminalisation, with the possibility of prison sentences), as under the US antitrust regime.

The European Commission (EC) is the institution responsible for cartel enforcement process in the EU regarding cartels affecting both competition in the EU and cross-border trade between member states. A detected cartel member may appeal the EC’s decision to the General Court (GC) that has both the power to annul, reduce or increase the fine imposed by the EC, as well as to review the entire investigation. In the second stage of appeals, the EC, a cartel member or both can appeal to the European Court of Justice (ECJ). The ECJ has the power to annul, reduce or increase the fines imposed by the GC; however, the ECJ does not have the power to reconsider the investigation by analysing facts and evidence that the GC used to corroborate its decisions Hellwig and Hüschelrath (2017) detail the cartel enforcement process in the European Union.

### Anti-cartel legislation in major European countries

#### Germany

In Germany, the anti-cartel law is the Act against Restrictions on Competition (ARC). Section 1 of the ARC corresponds exactly to Article 101(1) of the TFEU. The Federal Cartel Office (FCO) enforces the ARC and there are two separate proceedings according to the severity of the infringement. The FCO deals with minor infringements with just administrative proceedings included in the ARC. For more serious infringements, for which the FCO imposes fines, proceedings follow both the Code on Administrative offences and the Code on Criminal Procedure.

For the purposes of our paper, it is relevant to note that the German anti-cartel legislation prescribes sanctions for both firms and individuals. Prison sentences, of up to five years, are possible only for bid-rigging in tender proceedings. The maximum fine for a firm is equal to 10% of its worldwide turnover of the last completed business year. The maximum individual fine is EUR 1 million for serious violations (cartel activity, territory allocation, quotas, bid rigging) and EUR 100 000 for minor violations.

#### France

In March 2009, the President of the French Republic and Parliament made a reform (Lasserre, 2009) of the competition enforcement system, by creating an independent Antitrust Authority (Autorité de la concurrence). The current antitrust law underpinning the cartel enforcement process contemplates both corporate fines up to 10% of global turnover of the group to which a firm belongs to and individual sanctions (fines) of up to EUR 75 000 and/or imprisonment of up to 4 years (Autorité de la concurrence, 2016). These punishments are for all types of cartel activity (price fixing, market sharing agreements and bid-rigging). However, criminal convictions have been extremely rare.

#### United Kingdom

The 1998 Competition Act provides the legal framework within which the Competition and Markets Authority fights cartels, agreements between companies, decisions by associations of firms and concerted practices that restrict, prevent and distort competition within the UK. More specifically the Competition Act prohibits the following agreements and practices (Practical Law Competition, 2019):

• Directly or indirectly fix purchase or selling prices.

• Limit or control production, markets, technical development or investment.

• Share markets or sources of supply.

• Apply dissimilar conditions to equivalent transactions with other parties, placing them at a competitive disadvantage.

• Make the conclusion of contracts conditional on acceptance of unrelated obligations.

The Competition and Markets Authority can impose fines up to 10% of the firm’s global worldwide turnover in the last financial year. In addition, under the Enterprise Act 2002, individuals that arrange with other persons to implement actions such that two or more firms undertake cartel activity (price fixing, sharing markets or customers, limiting production or supply, or bid-rigging) may be imprisoned for up to five years. For cartel activity undertaken before 1 April 2014, for cartel conduct to be considered a criminal offence, attracting the prosecution of individuals, such individuals had to act dishonestly. The Theft Act 1968 defines the meaning of “dishonestly” (Practical Law Competition, 2019). The Court may disqualify for up to 15 years a corporate manager responsible for cartel activity. To sum up, individuals guilty of cartel offences may be subject to imprisonment and disqualification in their managerial roles.

### North American anti-cartel law

#### United States

The United States introduced antitrust law with the Sherman Act in 1890. In 1914, the US Congress created the Federal Trade Commission (FTC) with the Federal Trade Act. Any agreements or decisions between firms or individuals associated with fixing pricing, market division or bid-rigging always represents a violation (“per se” breach of the law) of the Sherman Act (Federal Trade Commission, n.d.).

The enforcement regime of antitrust laws is carried out by the FTC and the U.S. Department of Justice (DOJ) Antitrust Division and it is both civil and criminal in nature. Indeed, under the Sherman Act, both firms and individuals may be criminally prosecuted. Sanctions include corporate fines of up to USD 100 million along with individual fines of up to USD 1 million and a maximum of 10 years in prison. Criminal convictions are not uncommon. Moreover, the federal law allows an increase of the maximum fine up to twice the gains the conspirators have obtained or twice the monetary loss suffered by the victims if either of those two amounts is greater than USD 100 million (Federal Trade Commission, n.d.).

The Competition Act (14 months older than the US Sherman Act) is the relevant antitrust law in Canada. Section 45 of the Competition Act deems illegal any agreement and decision between individuals or companies leading to fix, maintain, increase or control prices, allocate markets, territories or custumers, or fix, maintain, control, reduce production or supply of a product. The Commissioner of Competition has the power to pursue antitrust investigations through the Competition Bureau. In case of solid evidence of a breach of the Competition Act, the case passes on the Public Prosecution Service for criminal prosecutions before either the Federal Court or the Courts of Province. The Federal Court or a Court of Province may impose a fine up to CAD 25 million and/or up to 14 years in prison. To convict an individual, the prosecutor must prove that such an individual has undertaken a cartel offence and had the intention of doing so (Competition Bureau, 2018).

### Cartel enforcement in practice

In this section, we review some legal practice by presenting cartel cases and enforcement processes for the European Union (France, Germany and the UK), Canada and the United States.

#### EU cartel case

The trucks cartel case (European Commission, 2017) gave rise to the highest fine levied by the European Commission since 1969: EUR 3.8 billion. The firms involved in the cartel were MAN, DAF, Daimler, Iveco and Volvo/Renault, with which the EC reached a settlement, and Scania, which refused to settle. Scania along with the other 5 companies established a cartel for a 14-year period, from 1997 to 2011.

The Commissioner for Competition, Margrethe Vestager, said: “This cartel affected very substantial numbers of road hauliers in Europe since Scania and the other truck manufacturers in the cartel produce more than nine out of every ten medium and heavy trucks sold in Europe. These trucks account for around three-quarters of inland transport of goods in Europe and play a vital role in the European economy. Instead of colluding on pricing, the truck manufacturers should have been competing against each other – also on environmental improvements” (European Commission, 2017).

The Commission’s investigation ascertained that between 1997 and 2004 senior managers of the involved companies met a number of times and held phone conversations as well. From 2004 to 2011, the truck firms’ German subsidiaries organised the cartel through electronic exchange of information. Overall, the cartel had the following goals: i) to co-ordinate prices at “gross list” for medium and heavy trucks in the European Economic Area (EEA); ii) to co-ordinate the timing for the introduction of emission technologies in compliance with the European emission standards; and iii) to pass on to consumers the costs associated with the adoption of the emission technologies.

The investigation was initiated after MAN applied for leniency. As a result, the EC carried out raids in January 2011. Subsequently, in November 2014, the EC issued a statement of objections. In July 2016, MAN, DAF, Daimler, Iveco and Volvo/Renault accepted the settlement decision. The EC levied a fine of EUR 1 billion to Daimler, EUR 881 million to Scania, EUR 753 million to DAF, EUR 670 million to Volvo/Renault and EUR 495 million to Iveco.

#### German price-fixing cases

We review two recent cases (Bundeskartellamt, 2017a; Bundeskartellamt, 2017b) entailing price fixing between manufacturer and retailer. The first case refers to a decision of the Bundeskartellamt (German Competition Authority) to fine two companies operating in the clothing industry EUR 10.9 million. Although the German anti-cartel law allows for individual fines, no individual was fined in this case.

The two companies involved in the proceedings were the clothing manufacturer Wellensteyn International GmbH & Co. KG (Wellensteyn) and the retailer Peek & Cloppenburg KG, Düsseldorf (P&C Düsseldorf). P&C Düsseldorf implemented the collusive agreement started by Wellensteyn and, as a reward, it received merchandise return options.2 Wellensteyn entered into agreements with retailers in Germany to maintain its minimum prices for products sold.

These agreements consisted of the prohibition of online sales and in the requirement for retailers to not reduce prices even at the end of the seasons. The manufacturer (Wellensteyn) monitored the prices charged by retailers to check whether they were adhering to the agreement. Moreover, retailers actively monitored competitors to ensure they were complying with the agreement. Complaints filed by some retailers prompted the antitrust investigation, which began in March 2013. The cartel was active between April 2008 and February 2013.

The second case involves vertical price-fixing in the sale of furniture. The German Competition Authority imposed a total fine of EUR 4.4 million on 5 manufacturers and 4 managers. As a result, this case is a good example where both corporate and individual fines were applied. The companies fined were Hülsta-Werke Hüls GmbH & Co. KG, Stadtlohn, Rolf Benz AG & Co. KG, Nagold, Heinz Kettler GmbH, Ense-Parsit, Aeris GmbH, Haar, and Zebra Nord GmbH, Hatten-Sandkrug.

The five manufacturers established agreements with their retailers to maintain minimum prices as well as discount ranges to final consumers. The agreements dictated retailers to charge prices equal or greater than the recommended manufacturer price and included a monitoring system of retailers’ pricing strategies and a punishment system whereby the manufacturer would refuse to supply non-compliant retailers. For discretionary reasons, the Bundeskartellamt did not prosecute the retailers.

#### French cartel case

On 20 September 2010, the Antitrust Authority fined banks and financial institutions for violating Article 101 of the TFEU (Autorité de la concurrence, 2010). More precisely, they convicted these firms for colluding on interbank fees for cheque image exchanges and collecting those fees between 1 January 2002 and 1 July 2007. In particular, the authority imposed the following fines:

• Banque de France (French Central Bank), EUR 346 500 on the first breach and EUR 3 500 on the second.

• BPCE (resulting from a merger between the Banques Populaires (BP) and the Caisses d’Epargne (CE)) assuming the rights and obligations of BP Participations, EUR 37.7 million on the first breach and EUR 380 000 on the second.

• BPCE assuming the rights and obligations of CE Participations, EUR 52.3 million on the first breach and EUR 530 000 on the second.

• La Banque Postale, EUR 32.5 million on the first breach and EUR 330 000 on the second.

• BNP-Paribas, EUR 62.7 million on the first breach and EUR 630 000 on the second.

• Crédit Agricole, EUR 82.1 million on the first breach and EUR 830 000 on the second.

• Crédit Mutuel, EUR 2.9 million on the first breach and EUR 30 000 on the second.

• Crédit du Nord, EUR 6.9 million on the first breach and EUR 70 000 on the second.

• Crédit Industriel et Commercial, EUR 20.9 million on the first breach and EUR 210 000 on the second.

• LCL (former Crédit Lyonnais), a subsidiary of Crédit Agricole, EUR 20.7 million on the first breach and EUR 210 000 on the second, for which Crédit Agricole is held responsible for EUR 15 million on the first breach and EUR 152 000 on the second.

• HSBC, EUR 8.9 million on the first breach and EUR 90 000 on the second.

• Société Générale, EUR 52.9 million on the first breach and EUR 530 000 on the second.

UK cartel case

At the end of March 2016, the Competition and Markets Authority (CMA) opened an investigation into two segments of the market for furniture: supply of drawer wraps and drawer fronts at the manufacturers’ level (CMA, 2016). Regarding the first product (drawer wraps), three companies, Thomas Armstrong (Timber) Ltd, Hoffman Thornwood Ltd and BHK (UK) Ltd have been found guilty of cartel arrangements. As BHK has applied for leniency, the CMA did not impose a fine on this firm, conditional on its continued co-operation with the investigation.

In what concerns the second product (drawer fronts), Thomas Armstrong (Timber) Ltd and Hoffman Thornwood Ltd have admitted their role in two other illicit cartels: one between 2006 and 2008, and the other between 2006 and 2008 and in 2011, to share the market and co-ordinate pricing strategies through bid-rigging, as well as share confidential and competitively sensitive information. The CMA imposed a total fine on the two companies of GBP 2.8 million.

#### Canada and the United States

The Antitrust Division of the DOJ has levied average annual corporate fines of USD 28 million in the early 1990s. Since 1994, average annual fines have increased dramatically to over USD 300 million, to reach USD 560 million in the period 2005-07. The average fine per firm has also increased significantly. In addition, individual sanctions – both fines and imprisonment – form an important part of the Antitrust Division’s punishment for cartel activity. Over the period from 1990 to 2007, the Antitrust Division of DOJ imposed jail sentences on 284 individuals (Shaffer et al., 2015; Connor, 2008b), with a mean of 24 per year over the period 2005-07 (Connor, 2008b); whereas, the mean annual number of fined individuals is 26.6 during the period of 1990 to 2006 (Connor, 2008b). In addition, individuals were fined an average of USD 147 100 (Connor, 2008b).

In 1889, Canada was the first country in the world to introduce the criminalisation of cartels. Nevertheless, defendants usually receive a suspended sentence. Therefore, the enforcement of individual sanctions for cartel offences has been “softer” than in the US. For instance, from 1998 to 2008, 11 individuals were convicted, nine of which paid fines.

### Literature review

The literature on the effect of antitrust jurisdictions on the likelihood of collusion is very recent.

#### Theoretical literature

Dargaud et al. (2013) develop an interesting theoretical analysis comparing two types of fines: a profit-based fine (like that used in most EU jurisdictions) and a delegation-based fine that targets the manager in a more direct way (as the one used in the USA). They find that a delegation-based fine is output-distortive but is more effective in deterring cartels. Their paper differs from our theoretical approach (described below) in three dimensions:

1. 1. They assume Cournot competition whilst we assume Bertrand competition.

2. 2. They focus on a duopoly whilst we focus on an oligopoly with N firms.

3. 3. The model is framed within the managerial delegation literature of Vickers (1995) and Fershtman and Judd (1987).

Within this literature, the manager is assumed to maximise a combination of firm’s profits and firm’s output, where the latter crucially depends on the powers delegated on the manager by shareholders (indirectly, by maximising this combination of profits and output, the manager is also maximising his own remuneration).

By contrast, in our approach, the (risk averse) manager maximises his (expected) utility, which depends on his remuneration consisting of a fixed and a variable (revenue-dependent) component. In other words, in Dargaud et al. (2013), the profit-based fine directly reduces firm’s profits and appears as a fixed cost in the manager’s objective function; by contrast, the delegation-based fine is a function of output and, not surprisingly, has output-distortive effects under collusion. In our case, as the manager is assumed to maximise his expected utility, the equivalents (in our setting) to a profit- or delegation-based fine directly affect the manager’s remuneration.3

In addition, Aubert (2009) addresses the interplay between managerial incentives to collude or compete and incentives to exert effort. The incentives to collude introduce distortions in managers’ effort, leading to internal firm inefficiency. In a model where managers privately choose market conduct (competition or collusion) and level of effort, high individual sanctions (monetary and imprisonment) for cartel behaviour deter collusion and incentivise deviations. Jail sentences are more efficient than individual monetary fines.

A recent body of the literature draws attention to the way in which fines can be calculated and its distortionary economic effects as well as their deterrence power. Dargaud et al. (2016) contribute to this literature by providing a theoretical analysis of the distortionary effects of two types of fines: profit-based and damage-based. Katsoulacos et al. (2015) also contribute to this discussion by providing a theoretical comparison of a fine based on the cartel overcharge with three other fine regimes: fixed fines, revenue-based fines and profit-based fines. Their analysis clearly lends support to an overcharge-based fine. Furthermore, Bageri et al. (2013) focus on distortions introduced by current methods of computing fines, whereas Katsoulacos and Ulph (2013) theoretically derive the optimal fine and study the impact on deterrence.

Our theoretical and experimental approaches involve shareholders who must design and offer wage contracts (with a fixed and a variable component, that is, with an underlying revenue-sharing mechanism) to managers. As such, our paper also contributes to the principal-agent literature. Related theoretical contributions in the economics literature involve revenue-sharing contracts in the video rental industry (Dana and Spier, 2001) and gate revenue sharing in team sports (Szymanski and Késenne, 2004). In addition, Wu (2017) theoretically explores the relationship and interplay between contracts that incentivise managerial effort the allocation of talent.4 The organisation theory literature studies revenue-sharing contracts in various professional services such as law, accounting, management consulting, advertising and architecture firms (Greenwood and Empson, 2003).

#### Empirical literature

The empirical literature devotes attention to revenue-sharing contracts in agricultural sharecropping (Allen and Lueck, 1992), flexible compensation which can serve as a device for risk-sharing as well as affect the financial structure of firms by encouraging stockholders to issue a greater amount of debt (Ichino, 1994) and box-office revenue sharing contracts as a device for flexible movie pricing in Spain’s distribution market (Gil and Lafontaine, 2012).

#### Experimental literature

Regarding the design of contracts, Anderhub et al. (2002) analyse a menu of contracts including fixed and flexible wage for studying incentive compatibility along with “fair sharing” and reciprocity. Fehr et al. (2007) study behaviour within a principal-agent framework where principals can choose among an incentive contract with enforceable monitoring, a bonus contract without fining and a trust contract. They find that about 90% of principals prefer to choose the bonus contract, in contrast to the standard theories of efficiency; also, effort exerted by the agents and the average payoff for both principals and agents is higher than in the incentive contract with monitoring.

The authors interpret these results as subjects caring about fairness and opposing situations of distrust and hostility created by incentive contracts with fining mechanisms. Moreover, Karakostas et al. (2017) study efficiency and fairness building on the work of Anderhub et al. (2002) and Fehr et al. (2007). They consider a revenue-sharing contract, a bonus contract and a trust contract among which principals can choose from. The vast majority of experimental subjects choose the revenue sharing contract and evidence suggests that such contract results in greater effort and a fairer distribution of profits, on average, than the bonus contract.

The experimental approach of our paper also extends the recent and relatively small experimental literature on cartels.5 Cooper and Kühn (2014) study three forms of communication and analyse which of these aids collusion in duopoly experiments. One of their key findings is that the type of communication involving contingencies facilitates collusion to a greater extent. In addition, Fonseca and Normann (2012) compare experimental Bertrand oligopoly markets with a varying number of firms and with and without communication, investigating how the number of firms affects collusion. As theory suggests, they find that the higher the price, the lower is the number of firms, both with and without communication. More interestingly, they find evidence that gains from communication are non-monotonic in the number of firms. Fonseca and Normann (2014), in a Bertrand-oligopoly experiment with endogenous cartel formation, find evidence that quadropolies form cartels more often than duopolies because of a smaller hysteresis gain if the cartel breaks down.

Among experimental contributions in the area of leniency programmes and cartel deterrence, Apesteguia et al. (2007), Hinloopen and Soetevent (2008), Hamaguchi et al. (2009) and Bigoni et al. (2012) are noteworthy. These experimental contributions assess the overall effectiveness and impact of leniency programmes on cartel activity. In particular, Bigoni et al. (2012) design an experiment for evaluating several antitrust policies: fines, leniency and rewards compared to a benchmark treatment with no antitrust law that the authors call “laissez-faire”. They find that, on the one hand, the presence of fines decreases the emergence of cartels and, therefore, displays substantial deterrence power; on the other hand, the existence of fines results in higher prices in comparison to cartels formed under “laissez-faire”, because cartel members appear to use the fine as a device for costly punishments. The treatment with leniency results in lower average cartel’s prices than antitrust without leniency mainly due to a smaller number of formed cartels; however, the authors do not find evidence of lower prices than those under the laissez-faire treatment, primarily because cartels formed under leniency appear to be more stable than cartels formed under laissez-faire. Under the rewards policy, the authors find evidence of prices declining to the competitive level.

#### Policy literature

Wils (2002; 2005) discusses individual sanctions and the criminalisation of cartels with reference to the EU context, concluding that imprisonment can lead to increase cartel deterrence. In addition, Bartalevich (2014) offers a comparative analysis of EU and US antitrust policy. Buccirossi and Spagnolo (2007) argue that although the introduction of individual criminal penalties can improve deterrence, well-designed and well-implemented leniency programmes can attain the same goal.

## Methodology

### Theoretical model

This section is based on a theoretical model developed by the authors and which we describe herein as simple a manner as possible, avoiding, to the extent possible, mathematical notation and highlighting the underlying economic intuition. This theoretical model was used to “calibrate” the experimental parameters, that is, the specific design of each of the experimental treatments (described below). In particular, the examples presented in this section borrow heavily from the instructions presented to subjects in the experiment and are particularly helpful to describe how the relatively complex setup that forms the basis of our theoretical model was conveyed to experimental subjects who, in most cases, have no economics background.

#### Market description

Consider an oligopolistic market with firms selling homogeneous goods and 𝐾 identical consumers. Each consumer wants to buy exactly one unit of the good. As goods are homogeneous, consumers will buy the good from the firm(s) charging the lowest price (as long as this price does not exceed the consumers’ reservation price – the maximum price that they would be willing to pay). Given the prices, there are two possible market configurations (see Box ‎4.2):

1. 1. If one firm charges a price 𝑝̌ below the prices charged by all the remaining firms, this firm supplies the entire market (as there are no capacity constraints) and rival firms sell nothing. The revenue of this firm is $p̌×K$ and the revenue of the remaining firms is zero.

2. 2. If there are $m\le n$ firms charging the same price 𝑝̌ and this price is lower than the price set by the remaining $n-m$ firms, the 𝑚 firms will equally split the 𝐾 consumers. The revenue of each of the 𝑚 firms is $p̌×\left(K/m\right)$ and the revenue of the remaining firms is zero.

Suppose that firms interact for an infinite number of periods and discount future profits at a constant (and equal across firms) rate. The choice of the price charged by each firm in each period is the responsibility of its manager. Managers are assumed to be symmetric, risk-averse and their utility only depends on their wages. Wages have two components:

1. 1. A fixed component, which the manager receives independently of the firm’s revenues in each period.

2. 2. A variable component, which corresponds to a percentage of the firms’ revenues in each period.6

Box ‎4.2. Example 1

Consider a market with $n=4$ firms (which we denote by A, B, C and D) and $K=24$ consumers that pay, at most, EUR 10 for each unit of the good.

1. 1. Suppose that Firm A sets a price of EUR 8.5, Firm B chooses a price of EUR 7.5, Firm C sets a price of EUR 8.8 and Firm D sets a price of EUR 7.6. As Firm B sets the lowest price, it sells all 24 units (at a price of EUR 7.5) and makes revenues of EUR 180 $\left(=24×7.5\right)$. Firms A, C and D do not supply any customer and, therefore, make EUR 0 in revenues.

2. 2. Suppose now that Firm A and Firm B both set a price of EUR 7, Firm C sets a price of EUR 8.8 and Firm D sets a price of EUR 7.4. As Firms A and B set the same (lowest) price, they share the customers equally. Hence, both firms sell 12 units at a price of EUR 7 each unit, each generating revenues of EUR 84 $\left(=12×7\right)$. As Firms C and D do not supply any customer, they make EUR 0 in revenues.

There are no costs of producing the good. Thus, in each period, the only cost for shareholders is the wage paid to managers. Consequently, the shareholders’ profit is the difference between the firm’s revenue and the manager’s wage.

For illustrative purposes, let us go back to Example 1 (Box ‎4.2) and see how managers’ payoffs would be calculated in that case.

Box ‎4.3. Example 2

Suppose that the fixed wage component is equal to EUR 30 and the variable component is 10% of the firm’s revenue.

1. 1. The managers of Firms A, C and D only receive the fixed component of their wage (as their firms make no revenues). Therefore, the wage of managers of Firms A, C and D is EUR 30 and the shareholders of these firms make losses – their payoff is -EUR 30. In contrast, the manager of Firm B receives the fixed component (EUR 30) plus 10% of his firm’s revenue (EUR 180). Therefore, his wage is equal to EUR 48 (=EUR 30 + EUR 18) and the shareholders of Firm B receive EUR 132 (=EUR 180 – EUR 48).

2. 2. The managers of Firms C and D only receive the fixed component (as their firms make no revenues), i.e. their wage is EUR 30. The shareholders of these firms make losses: their payoff is -EUR30. In contrast, the managers of Firms A and B receive the fixed component (EUR 30) plus 10% of the revenues of their firms (EUR 84). Thus, their wage is EUR 38.4 (= EUR 30 + EUR 8.4) and the shareholders of (each of) these firms receive EUR 45.6 (= EUR 84 – EUR 38.4).

Assume that the two types of players in the market – shareholders and managers – make their decisions according to the following timing:

1. 1. Each firm’s shareholders offer his manager a contract with a wage that contains a fixed as well as a variable component.7

2. 2. Each manager chooses whether or not to accept the contract offered by the firm’s shareholders. If the manager accepts the contract, he is the sole person responsible for setting the price of his firm in all periods. Otherwise, if he rejects the contract, he will receive a (fixed) income in all periods, which we denote by 𝑤𝑢 and refer to as “outside option income”.8

As the market duration is assumed to be infinite, managers will choose the price in each period in a way that maximises their discounted utility, given by the discounted sum of their (expected) wage in each period.

An important assumption we make – the reasoning for which becomes clear upon carefully analysing Examples 1 and 2 – is that shareholders themselves do not have an outside option. As we mentioned above, managers can choose not to accept the contract and receive the outside option income. However, we explicitly assume that shareholders cannot (or would not) design contracts that lead to the manager not accepting it, in which case the firm could not operate as it would have no manager.9

#### Competitive benchmark

Let us characterise the market outcome when managers set prices non-cooperatively. This is the equilibrium counterfactual, which would be observed if managers did not co-ordinate prices.

As is well known in the literature, if products are homogeneous and firms compete in prices, the non-co-operative equilibrium is a repetition of the Bertrand-Nash equilibrium of the stage game in all periods. Thus, in each period, the price will be equal to the marginal production cost (which is assumed equal to zero). If the contract has a non-zero fixed component, shareholders will incur losses in each period, because they will receive no revenues (as the price is equal to the marginal cost) but must pay the fixed wage component.

In this context, the key question we wish to address is: what contract will shareholders (optimally) offer managers? That is, anticipating how a firm’s manager will, in equilibrium, set the firm’s price, what contract would shareholders choose to offer to managers so as to maximise their payoff? In our competitive benchmark, the answer to this question is:

Result 1. Suppose that managers set prices non-co-operatively. Any contract with a fixed component equal to the outside option income is optimal (regardless of the variable component).

Let us understand the economic intuition behind this result. As shareholders aim at maximising profits (or, in this case, minimising losses), they want to set the lowest possible value for the fixed component. However, in order for managers to accept the contract, they must receive a discounted utility greater than or equal to the one they would receive if they rejected the contract (and received the outside option income in each period). It follows, therefore, that shareholders will offer a fixed wage component equal to the outside option income ( ${w}^{u}$). Finally, as the per-period equilibrium revenues are zero, the discounted utility for managers and shareholders’ profits do not depend on the value of the variable wage component.

#### Collusion

Looking at the competitive benchmark, it becomes clear that shareholders would strictly prefer that managers set their prices co-operatively if the variable wage component is relatively low.10 Let us then determine which contracts shareholders may offer to provide incentives for their managers to set prices co-operatively.

To ensure the tractability of the model, we focus on collusive agreements that involve the managers of all firms (full collusion). We will also focus on agreements aiming at co-ordinating all prices at the monopoly price level, i.e. the price that would prevail if there were a single firm active in the market (perfect collusion). It follows straightforwardly that the maximum price that managers may set is the consumers’ reservation price, which we denote by $p̅$. If all managers agree to set this price, each manager has the temptation to unilaterally deviate and set a price slightly below $p̅$. By doing so, the manager can supply the entire market (instead of sharing it equally with the other managers). Thus, for the agreement to be sustainable there must exist a credible punishment for managers that disrupt it. We assume the simplest punishment scheme: if a manager deviates from the agreement, it becomes permanently broken (i.e. there is no possibility for renegotiation after a deviation). In other words, after a deviation, managers will set prices equal to the marginal cost (which means zero revenues for the firms) forever and essentially revert to the competitive benchmark.

In order to obtain a price co-ordination outcome, shareholders must offer wage contracts such that:

• Managers are willing to accept, i.e. their discounted utility must be greater than (or equal to) the outside option income in all periods.

• Once the collusive agreement has been established, managers do not have unilateral incentives to disrupt the agreement (by slightly undercutting the price).

• Shareholders must prefer the price co-ordination outcome to the competitive benchmark, that is, shareholders’ payoffs must be higher when managers abide by the collusive agreement than when they set their prices non-co-operatively.

Shareholders will offer a contract that maximises their (discounted) profit subject to the above constraints. It is straightforward that the shareholders’ utility is decreasing in the fixed and variable component of the manager’s wage. Thus, shareholders will offer the lowest values for these components that the manager is willing to accept, i.e. in the limit, the fixed and variable components that leave the manager indifferent between accepting the contract and rejecting it. Given a contract, i.e. a combination of a fixed and a variable component, managers will accept it as long as their expected discounted utility is not lower than their discounted utility when they receive the outside option income in all periods.

It follows, therefore, that any contract that provides the same expected utility as the outside option income allows shareholders to extract the highest possible surplus from their managers (and still ensure contract acceptance). However, the terms of the contract, i.e. the way the wage is distributed between the fixed and variable components, affects the incentives for managers to co-ordinate prices.

As we have discussed above, our interest is in understanding how different antitrust regimes affect economic agents’ choices. Specifically, we will analyse how two different cartel fine policies affect the optimal contracts offered to managers. These two fine policies are inspired by the corporate fines regime that was observed until recently in most EU jurisdictions and on the individual fines regime that is observed in the US (in addition to its corporate fines). We do not examine the effect of the associated risk of imprisonment.

To make the two scenarios comparable, we will make similar assumptions. In both scenarios, we will assume that if the cartel is detected by the antitrust authority, managers may restart the agreement in the following period. In addition, there will be no aggravated fine if the cartel is caught again in a future period (for recidivism) and the probability of the cartel being caught is also not affected.11 We also assume that if the market is audited, enough evidence is collected for the antitrust authority to be able to convict the firms or managers in case of price co-ordination. This is modelled by assuming that with a given probability, the antitrust authority audits a market, detects the cartel if it is active and imposes a fine (on the firm or on the manager, depending on the antitrust regime). Deviators are assumed to also pay the fine if the market is audited and the cartel is detected.12

#### Corporate fines

For simplicity, under a corporate fine regime, we assume that cartel behaviour (if detected) is punished with a fine that targets firms, in the form of a percentage of its revenues. Also, for simplicity, this fine is assumed not to depend on the cartel duration. Suppose that, in a given period, the market is audited: if the managers are co-ordinating prices, a fine equal to a percentage of the firm’s revenues is imposed in all firms;13 if managers are not co-ordinating prices, then no fine has to be paid. Notice that if the variable wage component is positive, managers will be indirectly affected by the fine, insofar as they will receive a share of a lower “pie” (because firms’ net revenues will decrease in the amount of the corporate fine).

Box ‎4.4. Example 3

Suppose that, in every period, there is a 20% chance that the market will be audited. If the market is audited and managers are co-ordinating prices, the antitrust authority imposes a fine of 35% of the revenues of all firms. The managers’ contract is composed of a fixed component of EUR 30 plus 10% of the firms’ revenues (variable component). If all managers co-ordinate on the maximum price (EUR 10):

1. 1. If the market is not audited, the revenues of each firm are EUR 60 , the managers’ wage is EUR 36 and each shareholder gets EUR 24 .

2. 2. If the market is audited, the revenues of each firm are EUR 39 , the managers’ wage is EUR 33.9 and each shareholder gets EUR 5.1 .

As the market is audited with a probability of 20%, the expected wage of each manager is EUR 35.58 and the expected profit of each shareholder is EUR 20.22 .

As explained above, managers will only collude if their expected discounted utility when co-ordinating prices is greater than (or equal to) their expected discounted utility if they unilaterally deviate (i.e. if they slightly undercut the price to supply the whole market). An increase in the severity of the fine or in the probability of cartel detection has two countervailing effects on the incentives for managers to collude:

• On the one hand, the managers’ expected gains from collusion decrease because, with some probability, the firms’ expected revenues will be lower and, therefore, the managers’ variable wage component will be lower. This decreases the incentives for managers to collude.

• On the other hand, as deviations are still punished, the gain from a defection also decreases. This increases the incentives for managers to stick to the agreement.

In our theoretical model, once these two effects are taken into account, we obtain the following result:

Result 2. Under a corporate fine regime, shareholders will optimally offer fixed-wage contracts equal to the outside option income.

As shareholders are risk-neutral and managers are risk-averse, it is optimal to have all the risk on the shareholders’ side. Shareholders achieve such an outcome by offering a purely fixed contract (i.e. without a variable component). As shareholders have all the bargaining power when designing the contract, they will be able to extract all the managers’ surplus, i.e. they can offer wage contracts that leave managers with no surplus over their outside option income. With such a contract, managers will be indifferent between accepting and rejecting the contract (since they will receive the same utility) and, if accepting the contract, they will be indifferent between colluding or not (since they will receive the same utility regardless of the revenues of the firm).

#### Individual fines

Under an individual fine regime, such as in the US, cartel behaviour is punished with individual sanctions on the manager, as it is considered a criminal offence.14 Following Dargaud et al. (2013), we assume that this sanction is equivalent to a monetary reduction of the manager’s remuneration, e.g. the reputational damage caused by the fine.

We assume that the fine is a percentage of the manager’s wage and is independent of the cartel duration. Thus, with a positive probability, the market is not audited, and managers receive their (full) wage; but with a positive probability, the market is audited and if managers are co-ordinating prices, the cartel is detected and managers have to pay a fine (i.e. they receive a percentage lower than 100% of their wages).

As in the case of corporate fines, we assume that, if the cartel is detected, managers may restart the agreement in the following period. Furthermore, if managers disrupt the collusive agreement, they will have a short-run deviation gain but, after the deviation, they will revert to the competitive benchmark and permanently set a price equal to the marginal cost (which means zero revenues for firms).

Result 3. Under an individual fine regime, no fixed-wage contract provides incentives for managers to co-ordinate prices.

Box ‎4.5. Example 4

Suppose that, in every period, the market is audited with 20% probability. If the market is audited and managers are co-ordinating prices, all managers must pay a fine that corresponds to 10% of their wages. As in Example 3, the managers’ contract is composed of a fixed component of EUR 30 plus 10% of the firms’ revenues. As seen in Example 3, if all managers co-ordinate on a price of EUR 10, the revenues of each firm will be EUR 60. Thus:

1. 1. If the market is not audited, the manager’s wage is EUR 36 and each shareholder receives a profit of EUR 24 .

2. 2. If the market is audited, the manager’s wage is EUR 32.4 , each manager pays a fine equal to EUR 3.6 and each shareholder receives a profit of EUR 24 .

As the cartel is detected market with probability 20%, the expected wage of each manager is EUR 35.28 . Notice that shareholders bear no risk, as their individual profit is EUR 24, regardless of the market being audited or not.

Let us understand the intuition behind this result. Suppose that shareholders offer a fixed wage 𝑤̃ to the managers (i.e. managers receive the same wage regardless of their firm’s revenues) and managers agree to co-ordinate prices. In periods where the market is not audited, managers will receive 𝑤̃; but in periods where the market is audited, managers receive only a fraction of 𝑤̃ (as the fine falls on the manager). Suppose now that a manager unilaterally deviates from the agreement. In the deviating period, the manager receives 𝑤̃ if the market is not audited, and a fraction of 𝑤̃ if the market is audited. However, in all periods following the deviation, the manager will receive 𝑤̃ for sure (since managers will permanently revert to competition and, therefore, no further fines will need to be paid). Therefore, the expected discounted utility of a manager is surely higher if he deviates than if he sticks to the agreement. In sum, if managers receive a fixed-wage they will surely not abide by the collusive agreement.

Notice that Result 3 is in sharp contrast to the result in the case of corporate fines (Result 2). This occurs because, under corporate fines, the “costs” of the cartel are on the shareholders’ side. Thus, if the manager receives a fixed salary, his salary is the same regardless of whether there is price co-ordination (and the levying of corporate fines).

We also obtain the following result:

Result 4. Under an individual fine regime:

1. 1. If the discount factor is sufficiently high, any purely-variable contract (i.e. without fixed component) provides incentives for managers to collude. As a result, the optimal contract is the purely-variable contract that leaves managers with the same expected discounted utility as if they rejected the contract (and received the outside option income in each period).

1. 2. For lower values of the discount factor, the optimal contract must have strictly positive fixed and variable components. Among all possible contracts with positive fixed and variable components, shareholders would like to offer the contract that makes collusion among managers more likely.

Let us grasp the intuition behind Result 4. Under an individual fines regime, a wage contract without variable component does not provide incentives for managers to collude (Result 3). Thus, the question is whether a purely variable contract is optimal or not. If the discount factor is low, a contract without fixed component is not optimal because managers do not place much value in future payoffs and will not resist the temptation of disrupting the agreement to (significantly) increase the revenue of their firms in the present (and, therefore, their wage). As a result, when the discount factor is low, the contract must have both variable and fixed components strictly positive. If the discount factor is high, this temptation for unilateral deviation vanishes.

### Experimental design

To answer our research questions, we develop and implement a computerised experiment involving experimental four-firm markets, where subjects play a repeated Bertrand game with inelastic demand and identical firms selling a homogenous product. We choose experimental markets with four firms because for such markets we have experimental evidence of having greater gains and higher incentives from explicit collusion (Fonseca and Normann, 2012; 2014). The marginal cost is assumed to be 0 for simplicity, and we assume a mass of simulated consumers $M=24$ with reservation price equal to 10. Consequently, subjects (firms) can charge a price between zero and ten. The firm charging the lowest price supplies the entire market; in case of ties, firms split the revenue evenly.

Furthermore, as subjects have the choice whether to start communicating via a chat messenger, we are able to endogenise cartel formation as in Fonseca and Normann (2014). Endogenising cartel formation allows us to study cartel prevalence, cartel effectiveness and cartel prices, which is one of the goals of this paper. We also assume the presence of an antitrust authority monitoring each market. Following Fonseca and Normann (2014) and various experiments on leniency programmes (e.g. Apesteguia et al., 2007; Hinloopen and Soetevent, 2008; Bigoni et al., 2012), the antitrust authority monitors each market with some probability, assumed to be $\tau =20%,$ in order to detect cartel behaviour. If a market is audited, we assume that a cartel, if active, is detected and the antitrust authority will levy a punishment which differs across jurisdictional frameworks. The cartel is formed only when all the four firms in a given market decide to communicate.

Our experiment consists of four treatments across two phases of a multi-day experiment. The four treatments are:

1. 1. a baseline treatment without communication, NoChat

2. 2. a treatment where firms may decide to form cartels without the threat of punishment, ChatNoLaw

3. 3. a treatment where individual fines are levied in case a cartel is detected, inspired by the US jurisdiction, ChatUS

4. 4. a treatment where corporate fines are levied in case of cartel detection, ChatEU.

In Phase 1, subjects play the role of managers in an indefinitely repeated Bertrand market with four firms. Following Dal Bó and Fréchette (2011), we simulate an indefinitely repeated market by imposing a 10% probability it will terminate at the end of each experimental period; the expected duration is therefore 10 experimental periods. This is a sufficiently long expected duration to allow for collusion to take place while keeping the expected total number of periods in the session as a whole (i.e. 40) low enough not to induce subject fatigue, which may compromise decision quality. Once a market ends, the software randomly rematches participants randomly into new sets of four and a new market starts. We do this four times to obtain four markets per session.15

At the start of the first period of each market, subjects are told the parameters of their contract, which determine their payoff. We implement two wage contracts, which differ in the revenue component. The two contracts are and , which we refer to respectively, as “high-powered” and “low-powered”. The rationale for the choice of these contract parameters is provided below.

To control for the possibility that the order in which we implement contracts may affect subjects’ decision-making, we implement two orderings at the session level: XYXY and YXYX. Subjects were compensated for the total earnings in two of the four markets in which they took part.

After the fourth market ended (i.e. at the end of Phase 1), subjects were told they would then take the role of firm owners. Their task would be to choose which of the two contracts they had just experienced as managers they would like to offer to a future manager of their firm. Their firm would exist in a future session of the experiment (Phase 2). Their earnings as firm owners would be equal to the revenue of the firm minus the manager salary minus any potential fine.

Ultimately, the main purpose of Phase 1 was to generate contract choices. Subjects played the role of managers in Phase 1 so that they had sufficient experience of the markets to make a better-informed choice of contracts when in the role of firm owner. We ran 6 sessions with 12 subjects for each of the 4 treatments, totalising 288 subjects and therefore generating 288 contract choices.

In Phase 2, subjects only played the role of managers, who were told that their contract was chosen by the firm owner, who was a participant in an earlier session. Every manager in a market in Phase 2 had the same contract. Managers were also told that the profits resulting from their pricing decisions would go to the firm owner. As in Phase 1, subjects took part in four indefinitely repeated markets with a continuation probability of 10%. In each market, they were assigned to a different firm owner, such that they were exposed to both types of contracts. We also implemented two orderings at the session level: XYXY and YXYX. In this second phase, we ran three sessions of each ordering type, with 12 subjects per session for each of the 4 treatments, for a total of 288 subjects.

The fine in both Phase 1 and Phase 2 markets was set at 35% of the firm’s revenue in the ChatEU treatment and 35% of a manager’s salary in the ChatUS treatment.

The sessions took place in the FEELE lab at the University of Exeter Business School between February and March 2018. The software used to run the experiment was z-Tree (Fischbacher, 2007). We recruited participants from a pool of volunteers using the FEELE lab’s ORSEE system (Greiner, 2015). Sessions lasted on average one hour. The average earnings were GBP 13.10 (min: GBP 9.00, max: GBP 19.00).

## Results and discussion

### Introductory note and test hypotheses

As mentioned above, each of the four treatments – NoChat, ChatNoLaw, ChatUS and ChatEU – was carefully designed, building on the results from our theoretical approach.

In the context of our research Goal 1 (“Do antitrust law regimes involving individual fines have larger cartel deterrence power than antitrust regimes encompassing only corporate fines?”), the main theoretical conclusion we arrive at is that for a given contract that a manager chooses to accept, it is indeed true that a corporate fine regime generates stronger incentives for cartel formation than an individual fine regime. That does not necessarily imply that cartels are expected to emerge for that given contract: the answer to this crucially depends on wage levels and on their impact in the manager’s incentive compatibility constraint – that is, on the difference between the expected (discounted) utility under a collusive outcome and the expected (discounted) utility in case of deviation.

This allows us to manipulate wage levels in such a way that a specific contract may generate incentives for collusion under one antitrust regime, but not under the other. Indeed, this is the underlying rationale for the wage level choices in the low- and high-powered contracts. Our expectation is that the low-powered contract generates incentives for collusion under a corporate fine regime (ChatEU) but not under an individual fine regime (ChatUS), because this contract is expected to satisfy the incentive compatibility constraint in the former, but not in the latter. By contrast, the high-powered contract was designed so that there are incentives for collusion in both regimes.16

Under the NoChat treatment, explicit cartel formation is not allowed, as there is no communication. By contrast, in the ChatNoLaw treatment, there is no punishment associated with cartels. Therefore, the incentive compatibility constraint is satisfied with both types of contract. Table ‎4.1 summarises these hypotheses.

Table ‎4.1. Summary of hypotheses

NoChat

ChatNoLaw

ChatUS

ChatEU

Low powered contract

No Cartels

Cartels

No cartels

Cartels

High-powered contract

No Cartels

Cartels

Cartels

Cartels

Following on from this line of reasoning, our hypothesis on cartel prevalence may be further refined, in particular because the crucial element underlying cartel formation is the incentive compatibility constraint. But managers may be heterogeneous (e.g. with different risk attitudes or with different discount factors): this implies that cartel formation may not be observed in the data even when it is theoretically expected to emerge. In order to understand this, recall that for a cartel not to be formed, all that is required is for a single manager to express his unwillingness to engage in communication with other managers. Theoretically, this would occur if that manager’s incentive compatibility constraint was not satisfied, which in our setup may only happen for manager-specific reasons, e.g. that manager’s risk attitude and/or discount factor may be very different from that of the remaining managers. Assuming that such manager heterogeneity may exist, but assuming it to be “equal” across treatments, that is, assuming that the same population of heterogeneous managers needs to make cartel formation decisions across treatments, we may conclude that cartels may not be formed when they are expected to be formed in Table ‎4.1. For instance, if one manager has a particularly low discount factor, he may “block” the emergence of (at least) one cartel in the ChatEU treatment. Naturally, that same manager with a particularly low discount factor would also block (at least) that cartel in the ChatUS treatment and, possibly, in the ChatNoLaw treatment. Therefore, building on the incentive compatibility constraint and on the possibility that managers are heterogeneous, we can refine Table ‎4.1 and posit the following hypotheses:

• Hypothesis 1. For a given contract (low-powered or high-powered), the number of cartels formed in the ChatNoLaw treatment should be higher than in the ChatEU treatment, which in turn should be higher than in the ChatUS treatment, and the latter should be higher than zero (the number of cartels formed, by definition, in the NoChat treatment).

• Hypothesis 2. In the ChatNoLaw, ChatUS and ChatEU treatments, the number of cartels formed should be higher with the high-powered contract than with the low-powered contract.

Regarding pricing behaviour, our theoretical framework is built upon the premise that managers, when they collude, choose the maximum price possible (“full collusion”). Indeed, taking into account that there is a punishment associated with cartels in the ChatEU and ChatUS treatments, it is perfectly logical that managers maximise their “upside”, that is, their collusive payoffs, because they face an expected cost. Similarly, in the ChatNoLaw treatment, expected utility maximisation dictates that managers should collude by choosing the maximum prices that consumers are willing to pay. Nevertheless, it may be that managers are able to co-ordinate on a different price level. The relevant aspect here is that the decision to form a cartel is heavily related to the incentive compatibility constraint, that is, the difference between the expected (discounted) payoffs of the collusive outcome and of a unilateral deviation. In short, if a cartel is formed, the incentive compatibility constraint must be satisfied. But in that case, it must also be true that colluding leads to higher payoffs than not colluding (and competing): the unilateral deviation payoffs are, in our theoretical approach, equal to those of Bertrand competition except for the deviation period. This means that if the incentive compatibility constraint is satisfied, then forming a cartel is preferable to Bertrand competition in the first place. Therefore:

• Hypothesis 3. Conditional on a cartel having been formed, managers should be able to co-ordinate on the same price level in the ChatNoLaw, ChatEU and ChatUS treatments, regardless of the contract type (low- or high-powered).

As mentioned above, at the end of Phase 1, managers were asked to play the role of firm owners and choose a particular contract that would be offered to managers in Phase 2. As firm owners, they would receive further payoffs depending on managers’ decisions in Phase 2. Looking at Table ‎4.1, it becomes relatively clear to outline our theoretical expectation for this choice. Clearly, from a theoretical viewpoint, we expect the manager incentive compatibility constraint to be satisfied in the ChatEU treatment regardless of the type of contract. Therefore, in that treatment, managers should have the incentives to collude, which implies that firm owners with a profit maximisation perspective should choose the low-powered contract – as it would be expected to achieve the same revenues but at a lower cost (the manager’s wage) to the firm owner. The same is true in the ChatNoLaw treatment. However, in the ChatUS treatment, the low-powered contract does not satisfy the incentive compatibility constraint. As such, in order to foster collusion, firm owners would need to choose the high-powered contract. We summarise this in the following way:

• Hypothesis 4. Given a choice between the low- and high-powered contracts, firm owners should choose the low-powered contract in the ChatNoLaw and ChatEU treatments, but the high-powered contract in the ChatUS treatment. They should be indifferent between the two in the NoChat treatment.

In order to test these hypotheses, we use only Phase 2 data, wherein subjects (managers) are making price and cartel formation decisions based on contracts that were chosen by real firm owners. The pricing/communication stage in Phase 1 was designed only to provide experience to those subjects in order for them to make an informed decision regarding their contract choice as firm owners, so we will only use those outcomes as predictors of contract choices.

### Cartel prevalence

We begin by looking at the frequency with which subjects agreed to form a cartel. We computed the total number of initiated cartels for each of the 216 four-firm markets in the ChatNoLaw, ChatEU and ChatUS treatments. Figure ‎4.1 displays the distribution of the number of unique cartels initiated during the lifetime of a market.

The NoChat and ChatNoLaw provide benchmark cases. In the former, cartels are never possible (therefore, zero cartels were formed during the lifetime of all markets), while in the latter there is no punishment associated with cartel formation (and, therefore, once a cartel is formed, it lasts until the market ends). As expected, all observations record either zero or exactly one cartel formed, in accordance with Table ‎4.1 and Hypothesis 1.

By contrast, in the ChatEU and ChatUS treatments, the antitrust authority may detect and break cartels (if formed), which means that more than one cartel may be observed over the lifetime of a market. Interestingly, in a significant percentage of markets, no cartels are formed in both treatments. Therefore, there would appear to be a significant deterrent effect from both individual and corporate fines. Overall, the distributions of cartel formation are very similar in the ChatEU and ChatUS treatments for both high-powered and low-powered contracts. To test for this, we regressed the number of cartels formed in a given market on a dummy for high-powered contracts, a dummy for ChatUS, as well as a set of market dummies to account for learning effects. We omit the NoChat and ChatNoLaw data since there is no variance in the outcome measure in these treatments. The results of the regression are summarised in Table ‎4.2.

There is no significant difference in the frequency of cartel formation between ChatEU and ChatUS either for low-powered ( $\left(1,11\right)=0.74,p=0.407$) or high-powered contracts ( $F\left(1,11\right)=0.25,p=0.630$). This means that Hypothesis 1 is not supported by the data in what concerns the ChatEU and ChatUS treatments. Also, there is no significant difference in the frequency of cartel formation between high- and low-powered contracts, either in ChatEU ( $\left(1,11\right)=0.33,p=0.578$) or ChatUS ( $F\left(1,11\right)=0.17,p=0.688$). This means that, in what concerns the ChatEU and ChatUS treatments, Hypothesis 2 is also not supported by the data.

Another way in which we can measure cartel prevalence is to quantify the extent to which cartels were active during the lifetime of a market. This analysis complements that of cartel formation, as it allows us to ascertain how long managers were prepared to wait before re-forming a cartel after it was detected. In the ChatNoLaw treatment, cartels were active in 96% of periods in which it was possible to form a cartel. In the ChatEU and ChatUS treatments, cartels were active in 59% and 63% of possible cases.

We regressed a variable equal to the proportion of periods where a cartel was active in a market on a dummy for high powered contracts (HighPowered), a set of treatment dummies (ChatEU, ChatUS) and their interaction with HighPowered, and a set of market dummies (Market2, Market 3, Market 4) that account for any learning across markets. Results from the regression are available in Table ‎4.2.

Table ‎4.2. Determinants of cartel formation coefficient and statistical significance (standard errors)

Dependent variable:

Cartels started

Active cartel

High-Powered Contract

-0.138 (0.242)

-0.017 (0.074)

ChatUS

0.222 (0.258)

0.011 (0.063)

High-Powered Contract x ChatUS

-0.111 (0.269)

0.043 (0.085)

Market #2

1.583*** (0.212)

0.349*** (0.064)

Market #3

0.917*** (0.158)

0.404*** (0.055)

Market #4

1.000*** (0.160)

0.343*** (0.054)

Constant

0.681*** (0.159)

0.233** (0.081)

R2

0.278

0.257

N

144

144

***: significant at the 1% level.

Note: Robust standard errors clustered at the session level in parentheses.

Source: Gonçalves, R. et al. (2018), “Cartel deterrence and manager labour market in USA and EU antitrust jurisdictions: Theoretical and experimental evidence”, Unpublished, Research Paper for the OECD, Católica Porto Business School, Porto.

Cartels are not more prevalent in the ChatEU treatment than in ChatUS treatment, both for low-powered contracts ( $\left(1,17\right)=0.03,p=0.862$) and high-powered contracts ( $F\left(1,17\right)=0.59,p=0.451$). Again, the evidence does not appear to support Hypothesis 1 (relative to these 2 treatments). We also do not detect a difference in the prevalence of cartels as a function of manager contracts in the ChatNoLaw ( $F\left(1,17\right)=1.63,p=0.219$), ChatEU ( $F\left(1,17\right)=0.21,p=0.650$) or ChatUS ( $F\left(1,17\right)=0.04,p=0.851$) treatments. This also implies Hypothesis 2 does not appear to be supported by the data.

We next document the voting decisions taken by managers whenever the opportunity to form a cartel arose. Remember that cartels were only formed if there was a unanimous decision by managers. Figure ‎4.2 displays the distribution of voting outcomes in each treatment.

In the ChatNoLaw treatment, the overwhelming proportion of outcomes was a unanimous agreement to form a cartel. Since there was no cartel detection, the number of votes is substantially lower than in the ChatEU and ChatUS treatments, as there were fewer opportunities to vote in favour of cartel formation (if formed, a cartel would only break down when the market ended). The distribution of voting outcomes in the ChatEU treatment is similar to its counterpart in the ChatUS treatment. We estimated random-effects models of the individual decision to vote in favour of forming a cartel whenever that vote was available to managers in a market – that is, excluding the very first period in a market, as well as any period in which the cartel was already active. The regressors are dummy variables for whether the cartel had been caught in the 4 previous periods (𝑡−1, 𝑡−2, 𝑡−3 and 𝑡−4), a dummy for ChatEU, a dummy for high-powered contract and its interaction with the ChatEU dummy, as well as 3 market dummies. Results are presented in Table ‎4.3.

Table ‎4.3. Determinants of individual and aggregate votes for cartel formation coefficient and statistical significance (standard errors)

Dependent variable:

Individual vote

Caught (t-1)

0.361*** (0.047)

1.771*** (0.182)

Caught (t-2)

0.261*** (0.044)

1.377*** (0.207)

Caught (t-3)

0.086** (0.038)

0.596*** (0.184)

Caught (t-4)

0.051 (0.038)

0.197 (0.159)

ChatEU

-0.011 (0.031)

-0.028 (0.212)

High Powered

-0.062*** (0.024)

-0.322** (0.127)

EU x High Powered

0.090** (0.036)

0.468 (0.285)

Period

-0.041*** (0.004)

0.014 (0.033)

Market 2

0.227*** (0.043)

-1.004** (0.391)

Market 3

0.610*** (0.050)

-1.625** (0.773)

Market 4

1.015*** (0.078)

-1.508 (1.082)

Constant

0.671*** (0.079)

1.648*** (0.364)

R2

0.14

0.230

N (# markets)

4 464 (144)

792 (144)

*: significant at the 10% level.

**: significant at the 5% level.

***: significant at the 1% level.

Note: Robust standard errors clustered at the session level. Data excludes the initial period of each market or any period in which cartel was already active.

Source: Gonçalves, R. et al. (2018), “Cartel deterrence and manager labour market in USA and EU antitrust jurisdictions: Theoretical and experimental evidence”, Unpublished, Research Paper for the OECD, Católica Porto Business School, Porto.

The results support the finding that cartels are most likely to re-form immediately after an audit takes place. The likelihood of a cartel being formed drops dramatically if it takes longer than two periods to reform. Interestingly, conditional on an audit having taken place, cartels are less likely to be formed under high-powered contracts in the ChatUS treatment but the reverse is true for the ChatEU treatment. This suggests that Hypothesis 2 for the ChatEU treatment appears to be supported by the data, but not for the ChatUS treatment. By contrast, as above, Hypothesis 1 does not appear to be supported by the data.

### Pricing behaviour

We now turn to pricing behaviour conditional on the cartel being active or not. We start by quantifying the proportion of periods in which firms were able to co-ordinate and charge the same price in a given period.

When firms could not or did not form a cartel, they were able to co-ordinate on a price in 6% of cases (2 instances in NoChat, 39 cases in ChatEU and 37 cases in ChatUS). In all cases, the price they co-ordinated on was 10. In contrast, firms were able to charge the same price in 57% of periods in which a cartel was active. Of those instances, the chosen price was almost always 10. The cases in which firms co-ordinated on a different price were (one observation each), as well as 5 and 4 (two observations each). Figure ‎4.3 displays the relative frequency of instances in which firms co-ordinated on the same price based on market-level averages.

To undertake the correct statistical inference, we must control for the market being played within a session, as well as the fact that markets are not statistically independent of each other. Results of the estimation are available in Table ‎4.4.

Table ‎4.4. Estimates on the propensity of managers to co-ordinate on the same price when a cartel is active

Dependent variable: SamePrice

Coefficient and statistical significance (standard errors)

ChatEU

-0.020 (0.090)

ChatUS

0.118 (0.102)

High-Powered

-0.116** (0.043)

High-Powered x ChatEU

0.067 (0.064)

High-Powered x ChatUS

0.114* (0.065)

Market 2

0.180*** (0.042)

Market 3

0.288*** (0.074)

Market 4

0.366*** (0.067)

Constant

0.338*** (0.086)

R2

0.16

N

196

*: significant at the 10% level.

**: significant at the 5% level.

***: significant at the 1% level.

Note: Each observation is the relative frequency of instances in a given market where firms all charged the same price and a cartel was active in that period. Standard errors are clustered at the session level.

Source: Gonçalves, R. et al. (2018), “Cartel deterrence and manager labour market in USA and EU antitrust jurisdictions: Theoretical and experimental evidence”, Unpublished, Research Paper for the OECD, Católica Porto Business School, Porto.

Conditional on a cartel being active, there is no statistically significant difference in the ability to co-ordinate prices across treatments between ChatUS and ChatEU when contracts are low-powered: ( $1,17\right)=2.38,p=0.142$; however, when contracts are high-powered, there is a marginally significant difference: $F\left(1,17\right)=3.52,p=0.078$). This implies that Hypothesis 3 is supported by the data in what concerns the comparison between these 2 treatments for a given contract. We also find that managers have greater ease in co-ordinating on prices in later markets than in earlier markets. In addition, we do find that managers in the ChatNoLaw treatment find it harder to co-ordinate on prices in high-powered contracts than in low-powered contracts ( $\left(1,17\right)=7.43,p=0.014$). A similar result was obtained in the ChatUS treatment ( $\left(1,17\right)=3.10,p=0.096$) but not in the ChatEU treatment ( $F\left(1,17\right)=1.08,p=0.313$). This implies that Hypothesis 3 is only partially supported by the data when we compare managers’ ability to co-ordinate prices within a treatment but across contracts: only in the ChatEU treatment do we find that the type of contract plays no role in managers’ ability to co-ordinate prices.

We now move to the analysis of the average selling price. Figure ‎4.4 displays the average selling price conditional on treatment, whether a cartel was active and the type of manager contract. We complement the figure with econometric analysis which accounts for time trends within a market as well as learning across markets. The econometric estimates are in Table ‎4.5.

Average selling prices are higher when cartels are active than when they are not. Focusing only on the former case, we find no significant difference across different antitrust regimes conditional on the type of contract. However, we do find an effect of contract type conditional on the antitrust regime: average prices in the ChatUS treatment are lower when manager contracts are high powered ( $\chi 2\left(1\right)=8.59,p=0.003$). Conversely, when cartels are not active, average prices in the ChatUS treatment are significantly higher when contracts are high-powered ( $\chi 2\left(1\right)=9.69,p=0.002$). This suggests that managers may have attempted more forcefully to collude tacitly after the cartel was detected in ChatUS than in ChatEU, because of the harsher punishment regime in the former treatment. Ultimately, the four-firm Bertrand environment is too competitive and frustrated those attempts. Understanding whether tacit collusion would have been successful in duopolies or triopolies is an interesting future line of inquiry.

Table ‎4.5. Estimates of the determinants of selling price

Dependent variable: Selling price

Coefficient and statistical significance (standard errors)

Active Cartel

5.686*** (0.527)

NoChat

-1.578*** (0.358)

ChatEU

-0.342 (0.250)

ChatUS

0.489 (0.373)

Active Cartel x ChatEU

-0.361 (0.697)

Active Cartel x ChatUS

-0.246 (0.731)

High Powered

-0.466** (0.219)

Active Cartel x High Powered

0.286 (0.413)

High Powered x NoChat

0.053 (0.402)

High Powered x ChatEU

0.896* (0.488)

High Powered x ChatUS

1.196*** (0.384)

Active Cartel x High Powered x ChatEU

-0.921 (0.698)

Active Cartel x High Powered x ChatUS

-1.629*** (0.556)

Initial Period

0.302 (0.224)

Period

0.047* (0.028)

Market 2

-0.333 (0.248)

Market 3

0.078 (0.434)

Market 4

-0.064 (0.694)

Constant

1.866*** (0.152)

R2

0.59

N (Markets)

2 736 (288)

*: significant at the 10% level.

**: significant at the 5% level.

***: significant at the 1% level.

Note: The unit of observation is the selling price of market j in period t. Standard errors are clustered at the session level.

Source: Gonçalves, R. et al. (2018), “Cartel deterrence and manager labour market in USA and EU antitrust jurisdictions: Theoretical and experimental evidence”, Unpublished, Research Paper for the OECD, Católica Porto Business School, Porto.

### Voting behaviour

We conclude the analysis by looking at contract choices made by firm owners. Figure ‎4.5 displays the frequency with which firm owners offered low powered contracts to managers.

In the NoChat, ChatEU and ChatUS treatments, the proportion of low powered contracts offered is 40%. In contrast, in the ChatNoLaw treatment, the proportion of low-powered contracts goes up to over 60%.

There is no significant difference in the frequency of low-powered contract choices between the NoChat and ChatEU ( $F\left(1,23\right)=0.18,p=0.677$); NoChat and ChatUS ( $F\left(1,23\right)=0.00,p=1.00$) and ChatEU and ChatUS treatments ( $F\left(1,23\right)=0.20,p=0.662$). The latter clearly provides evidence contrary to Hypothesis 4. In contrast, the proportion of low-powered choices in the ChatNoLaw treatment is significantly higher than in the NoChat ( $F\left(1,23\right)=10.40,p=0.004$), ChatEU ( $F\left(1,23\right)=12.46,p=.002$), and ChatUS treatments ( $F\left(1,23\right)=11.38,p=0.003$). This provides some evidence in support of Hypothesis 4 for the ChatNoLaw treatment.

To provide some additional information, we conducted a short unincentivised survey after the experiment had concluded. One of the open-ended questions pertained to the reasoning behind the contract choice. Based on the responses we came up with a series of categories, which we feel capture the responses.

The first category is Self Interest, which includes mentions of cost minimisation, or maximising profits, or simply stating selfishness as a motive. Examples of responses which were coded under this heading include: “More profit for me”; “Because the manager only getting 2% of the revenue means more revenue for me”.

The second category is Own Experience, which included instances where subjects referred to their own behaviour or outcomes in the markets in which they took part as managers as a justification for their choice. Examples include: “More money was made when variable pay was higher in my groups”; “I chose it because I earned more ECU in these sessions and so would hope that other people did too”.

The third category was Incentive in Contract to Collude (ICC), which refers to instances in which subjects explicitly referred to giving high-powered contracts in order to incentivise collusion explicit or tacit. Examples included: “Realised that if managers were acting rationally then my profit would be higher if the contract has 20% of revenue in, as it should encourage collusion”; “20% people more likely to co-operate, thus profits should be higher”.

Interestingly, a non-trivial proportion of subjects mentioned incentives, though not in the way the ICC is predicated to operate. Some subjects argued that low-powered incentives were less likely to induce deviations, which in turn should lead to more price stability. We categorised these instances as Incentives (Non-ICC). Examples include: “With a lower variable component, people tended to “go rogue” less as it paid off much less and so wasn’t worth it, so everyone stuck to putting 10. This means there would be a greater chance of picking a firm that had some form of profit”.

We also categorised under this heading entries that referred to incentives that related to pricing behaviour but did not explicitly mention the formation of cartels. Examples include inducing more competitive behaviour: “So that the manager would more carefully choose his price, since he would be receiving a considerable portion of the revenue if his price was the lowest”; “I wanted to motivate the manager not to co-operate”; or “The 20% variable was a higher motivation to make better sales to the consumer using an established unit price. I was more encouraged to think about my decision if more was to potentially be earned”.

Another category we generated was Altruism, which refers to instances where the subject expressed concern for the welfare of the manager, or general welfare. Examples include: “20% is the nice choice for managers”; “Give the other manager an opportunity to earn as much as possible”; or “Feels more ethical even in a simulation. Plus, it means that the people who play in the future have more of a chance of receiving ECU in revenue”. All other instances are summarised under Other.

Table ‎4.6 summarises the relative frequency of each coding category for each of the four treatments. In all treatments, the most frequently cited motive is narrow self-interest, expressed either via minimising the amount paid to managers or as maximising own payoff in a narrow, non-strategic sense (in that the potential gains from collusion are not explicitly mentioned). In NoChat and ChatNoLaw, incentivising the manager in a generic sense is the second most frequently used motive, closely followed by motivating the manager to engage in collusion, which becomes the second most frequent motive in ChatUS and ChatEU. Importantly, other-regarding concerns account for a sizeable fraction of responses, as does the firm owner’s experiences in the role of manager as to what was the most profitable environment.

This may help understand why we do not observe a larger difference between ChatUS and ChatEU in the fraction of high-powered contracts: not enough firm owners were either motivated or sufficiently strategically sophisticated to understand the potential for motivating managers through their contract choice.

Table ‎4.6. Relative frequency (%) of self-reported motives for contract choice NoChat

NoChat

ChatNoLaw

ChatEU

ChatUS

Overall

Altruism

8

8

10

7

8

ICC

11

7

14

18

13

Incentives (Non-ICC)

13

11

8

10

10

Own Experience

4

4

7

14

7

Self-Interest

36

56

32

32

39

Other

28

14

29

19

23

Source: Gonçalves, R. et al. (2018), “Cartel deterrence and manager labour market in USA and EU antitrust jurisdictions: Theoretical and experimental evidence”, Unpublished, Research Paper for the OECD, Católica Porto Business School, Porto.

There are two important issues to take from the contract choice data. First, while low-powered contracts do (theoretically) provide the incentive to collude in the ChatEU treatment, it appears that 60% of firm owners do not choose that contract (to offer to managers). This contradicts Hypothesis 4 regarding the ChatEU treatment.

An alternative explanation for the high percentage of high-powered contracts is reciprocity manifested through gift exchange: firm owners could offer a generous contract to managers in the expectation that the latter will reciprocate with higher (attempts at) collusion. However, the higher frequency of low-powered contracts in the ChatNoLaw treatment undermines that explanation. The gift exchange hypothesis should predict the same behaviour across treatments: if firm owners want their manager to collude, they should be generous. The (standard) game-theoretic approach says the opposite: firm owners should not offer high-powered incentives unless there is an incentive-compatibility constraint to satisfy and managers need to be incentivised to collude. This is borne out by the data: in the ChatNoLaw treatment, there is no inherent downside risk in communicating and communicating greatly facilitates collusion. Therefore, the managers’ incentive-compatibility constraint is always satisfied and we observe more low-powered contracts being offered than in the ChatEU and ChatUS treatments, where managers face the risk of being fined if they communicate.

Whilst the NoChat treatment is (apparently) puzzling, recall Hypothesis 4 in that regard: the contract choice should make no difference to firm owners. Therefore, one should expect an approximately equal number of low- and high-powered contracts being chosen. They anticipate that managers will play the Bertrand-Nash equilibrium of the stage game (i.e. $p\le 0.01$) so the expected loss from the variable component of the wage is negligible. This justifies their choosing such a high proportion of high-powered contracts.

### Discussion

We find that both individual and corporate fines have some success in deterring managers from forming cartels, however, by and large, the experimental results provide very little support to the theoretical predictions we made. Therefore, it is important to understand why this is so. Whilst we do not provide a definite answer here, we point to potential explanations that may help in understanding in what ways (and why) experimental subjects may diverge from our theoretical expectation.

Let us start by considering the decision to form a cartel. Our theoretical approach suggests that managers should base their decision on the sign (positive or negative) of the following expression, where 𝑈 represents each manager’s expected discounted utility (cartel formation constraint):

$Ucollusion-Ucompetition$

Similarly, once a cartel is formed, a manager’s decision to abide by the cartel agreement instead of deviating and undercutting the agreed price should depend on the sign (positive or negative) of this expression (incentive compatibility constraint):

$Ucollusion-Udeviation$

These two expressions depend on several variables as well as several assumptions. Let us start with the variables, some of which are “controlled” through experimental parameters, whilst others are manager-specific. The experimental parameters that affect these expressions are: the contract (fixed and variable component), the type of fine (individual or corporate), the magnitude of the fine, the probability of cartel detection, the discount factor, the number of consumers, the maximum price they are willing to pay and the number of firms in each market. The above description of our experimental design explains in detail the specific parameters chosen for each of these variables.

But there is one variable that is manager-specific, that is, which cannot be “controlled” in the experiment and which depends on each individual: the manager’s risk aversion. A more risk-averse manager will have (all else equal) a lower expected utility of a “lottery”, that is, of a specific random event that may affect his final outcome. For example, take a coin toss: with 50% probability it lands “heads” and the individual wins EUR 10 and, with 50% probability, it lands “tales” and the individual wins nothing. The more risk-averse an individual is, the lower will his expected utility associated with this coin toss be. Applying this to our setup, this implies that more risk-averse individuals will have lower expected utilities associated with the collusive, the deviation and the competition outcomes. Whilst, on its own, an increased risk aversion will affect all outcomes in a similar manner, thus preserving the sign of the above expressions, that may not be the case in conjunction with other “deviations” from our theoretical approach.

In our experimental design, we have relied on our theoretical approach and assumed that all managers had a similar degree of risk aversion as well as a similar discount factor. In combination with the remaining “experimental” parameters, this allowed us to determine the sign of the above expressions and, thus, to determine, in each treatment and for each contract, whether or not we expected cartels to emerge (and subsist over time). Therefore, one possible explanation for the discrepancy between our theoretical predictions and our experimental results may be associated with manager heterogeneity: heterogeneity in the risk aversion parameters and heterogeneity in the strategies chosen under each circumstance.

Recall that, in the experiment, a cartel would be formed if all members agreed to form the cartel. Under our theoretical approach’s assumption of symmetry among managers, if the above expressions were positive for a manager, they would be positive for all managers. But clearly, all that is necessary for a cartel not to emerge in the experiment is for one of the two above expressions not to be positive for a given manager. And this could happen because his risk aversion parameter in combination with other “deviations” from our theoretical approach is significantly different from those of the remaining managers. If that were the case, we would expect a cartel not to be formed, although the number of “votes” to form a cartel was very high. When we look at our results for cartel prevalence, it becomes clear that this may be one possible explanation for our results: when we consider only the number of cartels formed, neither Hypothesis 1 nor Hypothesis 2 are supported by the data. However, when we look instead at the number of votes to form a cartel, Hypothesis 2 is supported by the data in the ChatEU treatment. This means that manager heterogeneity may help in explaining the divergence from our theoretical expectation.

It is therefore important to understand what other “deviations” from our theoretical approach may explain the observed results. These “deviations” are linked with the theoretical assumptions made when evaluating the sign of the above expressions. Let us start with $Ucollusion$, that is, the manager’s expected discounted utility along the collusive path. Our primary assumption is that once a cartel is formed, i) managers are able to co-ordinate on a single price and that ii) that price is equal to 10, the maximum price consumers would be willing to pay for the good (full collusion). In other words, our underlying assumption for the cartel is that, if formed, it would successfully behave as a monopolist. Also, this implies that the cartel would generate the highest possible payoff that any co-ordination strategy could achieve. From an economic viewpoint, as we have discussed above, this is logical. However, the data suggests that this was not the only co-ordination strategy used, although it was, by far, the most prevalent.

Regarding $Udeviation$, the manager’s expected discounted utility if he disrupts the agreement, the main assumption made is related to the periods subsequent to the deviation period. In particular, if a manager deviates from the cartel agreement (whichever it is, that is, whatever is the agreed price level), his firm captures the whole market in the deviation period, but is then likely to be punished by the remaining cartel members in subsequent periods. The assumption we have made was that the remaining cartel members reverted to the Bertrand-Nash equilibrium strategies in all subsequent periods. That is, all chose a price of zero in all periods after an observed deviation. Whilst this is a standard assumption in the literature, it is also true that it is the harshest possible punishment that the remaining cartel members can impose on someone who deviates. In addition, whilst this is undoubtedly a punishment on a deviator, it also affects the remaining cartel members, whose firms are thus assumed to receive no revenues until the market ends and its managers are assumed to receive only the fixed component of their wages. Although we do not report this above, there are several cases of cartels that subsisted even after a deviation. In other words, in those cases, a deviation did not trigger the Bertrand-Nash equilibrium. Casual observation of the experiment as it was evolving suggests that managers continued to talk with one another after a deviation occurred. In some cases, the remaining cartel members would inquire about the deviator in order to understand why that happened. And in several cases, all managers were able to co-ordinate prices again. Clearly, in those cases, $Udeviation$ would be higher than we predicted and this would affect the incentive compatibility constraint. In other words, this may affect cartel survival and help explain why it was that firms were only able to co-ordinate on prices in 57% of all periods in which a cartel was active.

In addition, whether or not “punishment strategies” differed across contracts may also help explain our results. For example, suppose that the reversion to Bertrand-Nash equilibrium strategies is more likely in the low-powered contract. This could be rationalised because with the low-powered contract, the variable component was low and, therefore, the difference (in utility) between a punishment strategy based on reversion to Bertrand-Nash equilibrium strategies or an alternative strategy (including, for instance, the possibility that the agreement is re-enacted) is also low. In that case, one would expect price co-ordination to be more difficult under high-powered contracts. With a higher variable component: a manager knows, when deviating, that everyone will be hurt if there is a reversion to Bertrand-Nash equilibrium strategies and may thus find it easier to convince the remaining cartel members to re-enact price co-ordination, which will increase firms’ revenues and, through the variable component, managers’ payoffs. Therefore, all else equal, after a deviation occurs, one could expect more successful price co-ordination with high-powered contracts.

Finally, our main assumption associated with $Ucompetition$, the manager’s expected discounted utility if there is no price coordination, is that managers choose the Bertrand-Nash equilibrium strategies, i.e. they set a price of zero, which generates no revenues and managers only receive the fixed component of their wages. This is a crucial assumption to determine whether or not a cartel is formed, as it will affect the sign of the first expression above (cartel formation constraint). There are two dimensions associated with this assumption: a first when we think of a cartel being formed for the first time; and a second when, within a market, we think of a cartel formation decision after it has been detected.

Consider the decision to form a cartel for the first time. Arguably, this is when the assumption of Bertrand-Nash equilibrium strategies makes more sense: managers have not yet communicated with one another and will have observed “market behaviour” in those periods. It may be that Bertrand-Nash equilibrium strategies were not played, but it is very likely that prices will have been relatively low.

By contrast, after a cartel has been formed and detected by the competition authority, managers will know their co-operation history. In particular, they will know whether or not they were successful in co-ordinating prices whilst the cartel operated. Therefore, it is possible that after the cartel was detected, cartel members no longer feel the need to explicitly communicate again (and still be able to set high prices). Explicitly forming a subsequent cartel by accepting to communicate exposes members to the risk of being detected (and fined). If they can successfully coordinate prices without explicit communication, they may well prefer to do so. Naturally, this means that tacit collusion is enacted. In other words, it may be that $Ucompetition$, either because managers do not choose Bertrand-Nash equilibrium strategies or because they tacitly collude, is higher than we theoretically predicted and this may explain why it was that in the ChatEU and ChatUS treatments there were several instances where cartels were not re-enacted after detection. In addition, it may well be that such alternatives to Bertrand-Nash competition were more likely with a particular type of contract. As above, with high-powered contracts, managers may be more likely to engage in alternative strategies other than Bertrand-Nash competition in order to generate revenues for their firms which, indirectly, benefit them through the variable component of their wages.

We do not think that, on their own, either of these explanations is sufficient to explain our results. All may have played a role in explaining such a significant divergence from our theoretical predictions. Naturally, it is our intention to explore this issue further in future research.

## Conclusion

This paper sets out to understand how the antitrust regime influences cartel behaviour. Specifically, our focus is on the punishment regime when cartels are detected: are there significant differences in cartel behaviour when the fines imposed are of an individual nature (levied on the firms’ managers) as opposed to being corporate in nature (levied on the firms’ revenues)? We combine this question with the particular characteristics of managers’ labour contract, namely the type of contract they are offered – fixed salary vs. fixed and a variable component – but also salary levels.

Our approach is both theoretical and experimental. In the theoretical approach, we develop a framework to analyse managers’ incentives to form and sustain cartels, as well as to determine firm shareholders’ optimal contract choices. We find that the different antitrust regimes induce different optimal contract choices by firms’ shareholders. In particular, shareholders choose fixed wage contracts under and antitrust regime with corporate fines but when fines are individual in nature, the optimal contract may contain a variable component or, in some cases, be purely variable.

In our experimental approach, we use our theoretical framework to carefully design an experiment where firms’ managers interact with one another in various different settings. We consider a setting where they cannot communicate with one another, as well as three settings where they can – one without the threat of punishment for collusion and two others where the punishment for collusion is either through individual or corporate fines.

Interestingly, while we find that both individual and corporate fines have some success in deterring managers from forming cartels, the experimental results diverge significantly from our theoretical predictions. These differences encompass: differences in the cartel prevalence; differences in the pricing behaviour; and, importantly, differences in the contractual choices made when subjects take on the role of shareholders.

In our brief discussion of possible factors underlying those differences, we point out that not only may managers not follow the strategies predicted in our theoretical framework (namely when reacting to a deviation from the collusive agreement) but they may also diverge from these in different ways. Manager heterogeneity – both in manager characteristics and in manager behaviour – may, therefore, be one of the main explanatory factors for the divergence between our theoretical predictions and experimental results.

Inevitably, our results provide more questions than answers and it is our intention to continue our research on this theme. Nevertheless, it is also our belief that by highlighting the significant differences between the theoretical models of collusion and observed (experimental) behaviour, we are contributing not only to the fine-tuning of those models but also to practitioners who are faced with real situations of collusion and need to make decisions.

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## Notes

← 1. Hellwig and Hüschelrath (2017), among others, confirm that the EC imposes only monetary fines.

← 2. Wellensteyn granted refunds to P&C Düsseldorf for clothes returned by costumers after purchase.

← 3. As Dargaud et al. (2013), we assume that the criminal sanctions directly applicable to managers in the US jurisdiction can be modelled as a utility reduction of the manager’s utility.

← 4. In equilibrium, the least talented are production workers, business owners are those gifted with low talent, managers receiving a bonus that does not vary with ability are medium talented, and managers paid with a flexible compensation that varies according to ability and firm size are highly talented.

← 5. Potters and Suetens (2013) provide a good review of Industrial Organization experiments since 2000.

← 6. The main element in the calculation of this variable component is the percentage of revenues that accrues to the manager, which, naturally, lies in between 0% and 100%.

← 7. Notice that one of these salary components can be equal to zero.

← 8. Naturally, managers who do not accept the contract may have several outside options to choose from, e.g. unemployment, employments offers in other markets, etc. For the purpose of our model, we assume that the best “outside option” has an associated fixed income per period.

← 9. To be more precise, all that we require is that the shareholders’ outside option yields a payoff that is lower than that which would be obtained when the firm receives no revenues and the shareholders’ payoff is negative in the amount of the manager’s fixed component. For example, a significant reputational cost could be assumed to exist and shareholders would incur it in case their firm is left without a manager. This would be sufficient to ensure that shareholders always design contracts that induce manager’s acceptance.

← 10. If the variable wage component is lower than 50%, this implies that for every additional EUR 100 in revenues, managers receive less than EUR 50 through their variable wage component and shareholders receive more than EUR 50 in additional profits. Therefore, an increase in firm’s revenues increases shareholders’ profits and thus contributes towards reducing the possible loss associated with the manager’s fixed wage component.

← 11. This is not entirely realistic but recidivism would introduce significant complexity into the analysis.

← 12. This assumption differs from Dargaud et al. (2013), who assumed that no fine is paid in the deviation period.

← 13. Recall that we only focus on collusive agreements that involve all firms.

← 14. To be more precise, the US antitrust regime is both a corporate fine and individual fine regime; that is, both coexist. In our model, we focus only on individual fines and assume corporate fines not to exist.

← 15. It is widely acknowledged in the experimental economics literature that subjects require repetition of a game in order to learn what the optimal course of action is. Dal Bó and Frechette (2011) argue that in the context of repeated games, it is necessary for subjects to also learn how to play the repeated game.

← 16. In relation to our previous remark – that a corporate fine regime generates stronger incentives for cartel formation than an individual fine regime – this implies that the incentive compatibility constraint is satisfied under both regimes with a high-powered contract, that is, the difference between the expected utility of the collusive outcome and a unilateral deviation is positive but it is higher (in magnitude) under a corporate fine regime.

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