Faculty of Economics and Business
MSc Economics: Markets and Regulation
The Effect of Individual Penalties on Destabilizing a Cartel A model including leniency programs
Author: Camiel Hekster (11045159)
Supervisor: Andr´ as Kiss
July 15, 2021
Statement of Originality
This document is written by Student Camiel Hekster who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it. UvA Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Various competition authorities try to minimize cross sectional cartel agreements amongst firms.
Companies that join together to fix prices, limit production or divide markets, negatively impact social welfare through less innovative incentives or anti-competitive pricing. This paper examines whether individual liability is a supportive tool to prevent such collusive behavior. Furthermore, a model that addresses the incentives of top and middle managers is established, to test individual leniency as an effective tool for an Antitrust Authority. There are several papers that try to in- vestigate optimal leniency programs, however no one has established a model including individual penalties for collusive behaviour. Given that various competition authorities already apply such penalties it is important to compare a theoretical model to existing literature with empirical proof of the effectiveness of individual liability. Furthermore, researchers have developed ideas around principle-agent problems within cartel agreements, however no one has yet established a model that considers the interaction between top and middle managers. Moreover, this paper answers the following question:
Does the implementation of individual sanctions have a destabilizing effect on cartel activity and what role does individual leniency play for the attractiveness of leniency application?
To answer this question I use a theoretical model based on a paper of Chen and Rey (2013).
This model is based on a duopolistic Bertrand model, where threshold level of profits are com- pared to argue upon stable cartel agreements. To include the destabilising effect of individual sanctions into my model, I consider these sanction as additional costs to a firm. Individuals in- volved in cartel agreements should be compensated for level of risk they face due to this additional individual liability. Compared to the paper of Aubert, C., et al. (2006), where they use the same method to investigate individual rewards, this paper includes an additional individual liability measure for the amount of compensation given by a firm. Furthermore, I consider three collusive strategies and test whether these strategies have any influence on the effectiveness of individual sanctions. Finally, there are some papers that give theories about principle-agent problems and the effect of individual leniency on business operations. This paper gives some additional perspective to these theories by building a model around individual cartel profits for top/middle managers to investigate the effectiveness of individual leniency. The model examines this tool in a game theoretical way taking into consideration a corporate governance structure, where top managers are assumed to have more incentive to apply for corporate leniency in stead of individual leniency.
A combination of corporate and individual liability in cartel prosecution turns out to be an effective tool towards the destabilisation of collusive behavior. The threshold level of stable cartel profits seem to increase once an Antitrust Authority has harsh individual punishment as a credible threat.
Also, independent of the timing of leniency or any collusive strategies, combining corporate and individual penalties can be an effective tool if an investigation is likely to succeed without cooper- ation. Besides individual penalties, individual leniency helps to align individual interest amongst managers towards antitrust compliance. The costs of collusion increase due to individual leniency since firms have to secure information and pay managers in order to secure their fidelity. The incentives of top/middle managers tend to evolve towards a race for corporate leniency within a firm and between the firms of a cartel. When the prosecution of collusive behavior lacks a high probability of detection due to limited resources, both individual liability and leniency turn out to be an effective tool if they are both established in competition policies.
The European Union (EU) and the United States (US) have been deeply involved in policy making with regard to detecting and prosecuting collusive behavior. Cartels and collusive behavior often come with monopolisation and a distortion of competition. Competition policies try to prevent such undertakings by setting a set of rules implemented by different authorities. An important difference between the US and the EU is the veriety in individual penalties. The European Com- mission and some individual European countries do not sanction individuals based on their cartel involvement, whilst the US introduced individual accountability such as imprisonment or individ- ual fines. Within the European Competition Network (ECN), European state members are allowed to implement their own sanctions which only apply to their country. Some countries within the EU impose fines on individuals that are held accountable for infringements of cartel prohibition, such as the Netherlands, Spain and Germany. Alternatively, there are also member states where individual accountability is punished by a prison sentence, like in the United Kingdom or Ireland.
There are also member states that follow the policy guidelines of the EU, such as Italy. This paper will briefly discuss these differences to better interpret the outcome of the model. Therefore, the structure of this paper is as follows. Section 2 of this paper compares different competition policies between the US and the EU. Section 3 considers different structures of cartel legislation and use these to form the assumptions of my model. Section 4 investigates the existing literature and argues why individual penalties are important in cartel prosecution. Section 5 elaborates on two different models and examines the effectiveness of different anti-competitive tools. Section 6 examines different papers to give my results some empirical support. Finally, Section 7 combines all findings and gives a policy discussion towards current competition authorities.
2 Competition Policy
In section 2, I give a brief overview of different competition policies and examine the differences in antitrust enforcement for both the US and EU.
2.1 Competition policy within the United States (US)
The oldest federal antitrust act within the US is the Sherman Act of 1890. It was adopted to regulate trust amongst suppliers and customers and includes concerns about unfair use of power and disparities in wealth (Fox, E., R. Pitofsky, 1997). The first section of this Act includes illegal concerns about conspiracies in restraint of trade, such as price fixing and market divisions. The second section makes it a violation to conspire with competitors to monopolize trade. However, a distinction is made between monopolizing behaviour and holding a monopoly position which is not prohibited by the Sherman Act (Fox, E., R. Pitofsky, 1997). In 1914, an additional Clayton Act was passed. This Act included additional legislation on business practices whose effect is to lessen competition or to create a monopoly. New principles were covered such as price discrimination, tie-in sales or exclusive-dealing. The US competition policy also includes the Robinson-Patman Act, which covers price discrimination and provision of services with greater detail. Finally, the Celler-Kefauver Act restricts mergers or joint ventures that lessen competition or tend to create a monopoly (Fox, E., R. Pitofsky, 1997). There are two agencies that ensure the application of these competition rules. The Department of Justice (DOJ) and the Antitrust Division are responsible for enforcing the Sherman and Clayton act. Besides this state enforcement, an additional private enforcement by companies or individuals that are injured in their business due to violations of the antitrust law, can sue on their own behalf (Fox, E., R. Pitofsky, 1997).
2.2 Competition policy within the European Union (EU)
The main objective of the EU competition rules is to enable the proper functioning of the Union’s internal market as a key driver for the well-being of EU citizens, businesses and society as a whole. To this end, the Treaty on the Functioning of the European Union (TFEU) contains rules that aim to prevent restrictions on and distortions of competition in the internal market (Fact Sheets on the European Union, 2020). Agreements between undertakings which have as objective to distort competition that affect trade between member states are prohibited (Article 101(1), TFEU) and automatically void (Article 101(2), TFEU). This includes explicit agreements such as cartels or collaborative practices on prices or limited production outputs. These practices are considered as harmful and prohibited without any exception. Exemptions to such agreements
are met when consumers are allowed a fair share of the resulting benefits (Official Journal of the European Commission, 2008). Article 102 TFEU prohibits one or more undertakings to abuse a dominant position in the internal market or in a substantial part of it. This dominant position is seen as an infringement of EU competition law if such a dominant position harms consumers and competitors alike (Official Journal of the European Commission, 2008). To enforce these competition rules, the European Competition Network (ECN), consisting of national competition authorities from member states and the Commission, serve as a platform to exchange information to achieve competition policy objectives.
3 Leniency Programs
In section 3, I will focus on the definition of leniency programs in order to compare different pro- grams across various countries. First, I will briefly discuss the leniency design of both the US and the EU, after which I will examine the main differences.
Leniency programs are designed to give incentives to cartel members to take the initiative to ap- proach the competition authority, confess their participation in a cartel and aid the competition law enforcers (UNCTAD, 2016). To get a better understanding of these leniency programs, we should first clearly define a cartel: A cartel is a group of similar, independent companies which join together to fix prices, to limit production or to share markets or customers between them. Instead of competing with each other, cartel members rely on each other’s agreed course of action, which reduces their incentives to provide new or better products and services at competitive prices. As a consequence, their clients (consumers or other businesses) end up paying more for less quality (European Commission, 2017).
Within such cartels, a company or individual within a company that is involved in these cartel agreements can act as a whistleblower. Once this is anonymously done, cartel participants generally faces a large or total reduction in penalties. Depending on the competition authority, those who come after the first whistleblower with decisive evidence can also benefit from reduced penalties or other incentives. To ensure an effective leniency program that incentivize leniency application, there are three essential conditions to be met before competition authority can successfully imple- ment such a program. First, competition law must provide the threat of severe sanctions for those who participate in hard core cartel activity. Secondly, members of a cartel must perceive a high risk of detection by the competition authority. Thirdly, market players should be able to predict with a high degree of certainty what consequences will be if they are caught colluding, and what treatment they can expect if they apply for leniency (UNCTAD, 2016).
The main objective of any leniency program is to destabilize cartels in order to avoid full market power amongst all participants. The idea is undermining trust between wrongdoers with the in- creased risk that one of them unilaterally reports to enjoy the benefits of the leniency programs (Spagnolo, 2004). Furthermore, social welfare effects such as limited competition and less techno- logical improvement are reduced as well as the costs involved in finding evidence for the authorities.
In a more theoretical way, the classical Prisoner’s Dilemma game is best comparable to a leniency policy. If there are two firms, both firms have the possibility to report the cartel to the competi- tion authorities or not. If both firms decide not to report the cartel, they both risk the possibility of cartel detection by the competition authority. In this case both receive a fine. If one reports the cartel, it will receive a reduced fine while the other firm pays the full fine. The best possible strategy for both firms is to report a the cartel and get a reduced fine or negotiate a plea deal.
3.1 Leniency programs within the US
In the original version of the DOJ, leniency programs date from 1978. The objective was to deter colluding practices. The program included complete protection against criminal prosecution to encourage leniency application. However, it was not very successful due to a small number of applicants. The major criticism to this leniency program was the lack of transparency. Protection from criminal prosecution was granted to the applicant, however amnesty was only awarded based on the DOJ judgement. This level of uncertainty would have prevented most firms from applying (Cloutier, 2013). To account for these transparency issues and increase cooperative incentives, the Antitrust Division revised the Corporate Leniency Policy in August 1993. Three major revisions were made to the policy: (1) leniency became automatic for qualifying corporations if the Division had no pre-existing investigation; (2) under certain circumstances, leniency was still available even if cooperation began after an investigation was underway; and (3) all officers, directors and employ- ees who came forward with the corporation to cooperate were protected from criminal prosecution (OECD, 2018). These changes were highly effective since there was a twenty-fold increase in the leniency application rate compared to the rate under the original policy.
Under the three factors that incentivize leniency application, the US Antitrust Division has im- proved their program for detecting cartel activity. In order to create deterrence, penalties to Sherman Act violations were raised over the years after the first leniency program. Similarly, dur- ing the late 1990’s, the deterrence was improved by introducing individual accountability. Also, the Antitrust Division has developed regulations to increase the risk of detection. They used tra- ditional criminal tools such as search warrants, subpoenas, consensual monitoring and wiretaps to
make sure that the rewards of self-reporting became to important compared to the risk of losing leniency to another cartel member (Werden, G.J., et al., 2012). To increase the transparency and increase treatment predictability after corporation, the Antitrust Division created an alternative leniency for corporations that come forward after an investigation has begun. There are two types of leniency provided by the Antitrust Division: (1) Type A Leniency where the illegal conduct is self-reported before a government investigation has begun; and (2) Type B Leniency where the illegal conduct is self-reported after an investigation has been initiated. Both types require the same conditions, however Type B leniency requires additional conditions where the Division does not yet have evidence against the company that is likely to result in a sustainable conviction and the Division determines that granting leniency would not be unfair to others (Lynch, N.E., 2011).
3.2 Leniency programs within the EU
During the late 1990´s the European Commission was well aware of the existence of detrimental effects of existing cartel agreements. However, the commission noticed that undertakings within cartel agreements were willing to end their participation, but were dissuaded from doing so by the high fines to which they were potentially exposed. This led to the first leniency program in 1996, that offered a favourable treatment to undertakings that were willing to cooperate. However, this policy was to be revised in 2002 due to low transparency and a lack of alignment between the level of reduced fines and the value of a company’s contribution (European Commission, 2002). The new guidelines of this second leniency program granted undertakings full immunity from any fines if it met several conditions. The first whistleblower would have to disclose sufficient evidence to carry out an investigation to prosecute the cartel. Also, during the Commission’s administrative procedure, the whistleblower was obliged to provide evidence on a continuous basis and was not allowed to take steps in coerce other undertakings to participate in the infringement. Finally, the Commission introduced the possibility of a fine reduction to a second or even third applicant that is able to provide evidence of the suspected infringement that added value to the existing evidence (European Commission, 2002). In 2006 a third leniency program was implemented, which consisted of a more detailed representation of the guidelines compared to the leniency program of 2002. The Commission introduced a more strict threshold level of evidence to the infringement that a partic- ipant would have to provide if they were willing to apply for full immunity. In particular, the new guidelines for providing evidence included a detailed description of the alleged cartel arrangement, including for instance its aims, activities and functioning, the geographic scope, the duration of and the estimated market volumes affected by the alleged cartel, the specific dates and locations
and participants in cartel contacts. The Commission also introduced a new systems where an applicant could be accepted on the basis of limited evidence and is granted time to improve their evidence to qualify for full immunity (European Commission, 2006).
Comparing these leniency programs between the EU and the US, both leniency programs agree upon the harmful consequences of any cartel activity. Both leniency programs were revised sev- eral times to improve transparency and cooperative incentives by awarding amnesty to the first applicant. Also, the cooperative incentives largely improved by introducing fine reduction to par- ticipants that provided value adding evidence once the investigation had already started. A final important parallel between both programs is that the first applicant should fully and continuously cooperate without the notice of other participants within the cartel agreement.
Besides these similarities between the EU and US leniency programs, there are also some differ- ences. In the program of the US, the first applicant to come forward with sufficient evidence receives full immunity from any fines, the second or third applicant does not receive any fine re- duction. While the European leniency program provides partial reduction in fines to the applicant that provides sufficient evidence once the investigation has started. Additionally, an important difference that led to this paper are the individual sanctions. The European Commission does not sanction individuals based on their cartel involvement, whilst the US introduced individual accountability such as imprisonment or individual fines. This difference will be discussed in the next section.
In the US, Section 1 of the Sherman Act (15 U.S.C.§ 1) prohibits any agreements amongst competi- tors that unreasonably limit competition. It outlaws every contract, combination, or conspiracy in restraint of trade and any monopolizing attempts. Price fixing, bid rigging, and market allocation are violations of Section 1 and are prosecuted criminally (US Department of Justice, 2018). Both individuals and businesses that violate this section may be prosecuted by the DOJ. These criminal convictions can result in a confinement or fines. These fines can be increased to twice the amount of what the cartel participants gained from their illegal acts. Apart from a corporate leniency policy, the US Antitrust Division has also set conditions under which the directors, officers and employees who come forward to cooperate will be considered for individual leniency. This only applies to individuals who approach the Division on their ow behalf and not as part of a corporate confession to report additional antitrust activity. Under this policy, ‘’leniency” means not prose-
cuting such an individual for their criminal activity within a cartel. Furthermore, the extent of any fine reduction is not only reflected by the timing of cooperation. Subsequent co-operators are able to plea negotiations with the DOJ. Plea bargaining can happen during investigations and possible fine reductions depend on the value that cooperation ads to the investigation. As a result, some cartel cases are settled before they go to court (US Department of Justice, 2020).
The European system of fining cartels with financial sanctions is more administrative. When a cartel is discovered by the European Commission without any participant applying for leniency, the Commission is allowed to determine the amount of fines that are imposed. These fines are assessed by taking a percentage of relevant sales. Relevant sales are sales that of the products covered by the infringement. Depending on the gravity of the infringement, the percentage that is applied on the relevant sales can be up to 30% (European Commission, 2006). Primarily, relevant percentages for cartels tend to be in the range of 15-20% . Depending in the duration, the percentage of value of the relevant sales is multiplied by the number of years and months the infringement lasted. This is seen as a good damage estimation that the cartel imposed on the economy. Furthermore, the Commission takes into account if the a company is a first time offender or if a company is a so called repeated offender and adjusts the fines upward accordingly (European Commission, 2006).
Another consideration to made by the Commission is the distinction between regular cartel mem- bers and ringleaders. Ringleaders can be described in two separate types: ‘instigators’ and the
‘leaders’. In the European legislation, cartel ringleader are sometimes eligible for amnesty, whereas the US legislation excludes such ringleaders from the leniency program (Bos, I., F. Wandschneider, 2012).
However, the European Commission is bounded to a legal maximum where the final amount of the fine is not allowed to be set higher than 10% of the annual turnover in the preceding business years of the infringement (European Commission, 2006). By applying for leniency a company can receive full immunity from fines and subsequent companies can receive reductions up to 50% of the fine that would otherwise be imposed. After the first applicant, the first subsequent applicant providing significant added value to the investigation can benefit from a 30-50% fine reduction.
Thereafter, the second applicant providing added value can benefit from a 20-30% fine reduction.
Finally, subsequent participants providing added value can benefit a fine reduction up to 20%
(European Commission, 2006). Additionally, like in the US, the Commission can offer a fine re- duction of 10% if it reaches settlement with a company. The foremost argument in favour of this reduction is the reduced administrative costs and the possibility of freeing up resources to open up new investigations.
4 Literature Review
In section 4, I give a brief overview of the relevant literature. First, I will focus on the theoretical contributions of the literature that compares leniency programs within a Bertrand or Cournot setting. Secondly, I conclude that the model of Chen and Rey (2012) is most suitable for the basic design of my model. Finally, I will briefly discuss the principal-agent problem in deciding on whom you should levy individual sanctions.
An article that is well known and referred to in most literature about leniency programs and cartel prosecution, is the article of Motta, M. and M. Polo (2003). In their article they study the enforcement of competition policy against collusion under leniency programs. The main objective is to investigate the deterrence (abstain from collusion) and desistence (comply with the authority for a certain period if found guilty) properties of a leniency program in antitrust cases. Moreover, they analyze if a fine reduction is the most desirable policy taking into account the costs of prosecution. Within their analysis they consider three different strategies. In the first one, there is no collusion between firms since each participant would prefer to deviate rather than joining in collusive agreements. Alternatively, firms collude and reveal once an investigation has been opened. Or they collude and do not reveal any information once an investigation is opened. To argue on the best collusive strategy, Motta and Polo (2003) include two probabilities into their model. The first includes the probability that the firms are reviewed by the Antitrust Authority and the second probability includes the probability of a successful investigation once the firms do not cooperate. It turns out that if both probabilities are sufficiently high, the best response of the firms is either to collude and reveal or not to collude, in which each firm would prefer to deviate due to a high probability of detection.
In line with the EU system of fining cartels, Motta and Polo (2003) find that the most effective leniency program includes the possibility of reduced fines once an investigation has already started.
Finally, the key takeaway from their findings points out the difference between resources within the Antitrust Authorities. With sufficient resources to prevent collusion using full fines, it turns out that leniency programs can have a pro-collusive effect. If there are limited resources, leniency programs may be optimal in a second best perspective. Also, it turns out that an optimal scheme requires full fines reduction for the first firm that collaborates with the Antitrust Division.
In the article of Chen and Rey (2012), they develop a model to resolve the trade-off between the contribution of leniency programs and the risk of generous leniency being exploited. They show that it is always desirable to offer some leniency in absence of any investigation. The effectiveness of leniency will diminish once an investigation with a reasonable likelihood of success is already
underway. When investigations are unlikely to succeed, due to patient cartels and robust collusive agreements, post-investigation leniency is likely to increase the success for these investigations.
Also, in line with most leniency programs, they show that it is optimal to offer less leniency once an investigation is already underway. Their paper is based on a Bertrand model, which will form the basis of my model. There main analysis is build around a duopolistic model, where two firms choose to either compete or collude with each other.
Spagnolo (2004) also examines the effect of leniency programs and their ability to deter cartels and organized crime by increasing incentives to ‘cheat’ on partners. Without any leniency program, they argue that welfare is maximized by setting the probability that a defecting firm is convicted to zero. Therefore, in absence of any leniency program, the antitrust authority should not impose any fines on firms that deviate from cartel agreements. With sufficiently high fines and zero probability of a defecting firm being convicted, firms are encouraged to defect from collusive behavior. After including leniency programs into their model, they find that sufficiently generous programs can be exploited by colluding agents. Agents may agree to report each period, enjoy leniency and avoid part of all fines. This effect increases the value of collusive agreements and reduced the deterrence effect of law enforcement policy (Spagnolo, G., 2004). While leniency contributes to destabilizing cartels, Spagnolo states that the optimal leniency programs should offer the first reporting agent a reward equal to the sum of all fines levied on other cartel members. Such a reward policy would mean full deterrence at no costs. Finally, if the antitrust authority cannot offer any rewards, Spagnolo shows that reduced fines for reporting firms can be useful in decreasing the cost of deviating from the cartel agreement.
A paper that expands this idea of positive rewards, is the paper of Aubert, C., et al. (2006). They compare the impact of reduced fines and positive rewards and argue that rewarding individuals can deter collusion in a more effective way. They argue that a sufficiently high reward (depending on the discount factor), is a more effective way to induce a firm to report collusion. However this rewarding system is bounded to some implementation issues. There might not be enough budget to commit to large rewards. However this argument is refuted with Spagnolo’s theory of rewarding an informant with a fraction of the fines paid by other firms of the cartel. Another issue that arises is political acceptance. The idea of rewarding guilty firms with large amounts of money may not be largely accepted. A final issue regarding large rewards, is the possibility of generating additional incentives to collude. If colluding firms take turns in reporting a cartel, it could become optimal to collude and systematically report. However, Aubert et al. (2006) give a credible argument that a reward should be restricted to the first informant. In terms of an individual rewards scheme, Aubert et al. (2006) argue that a company would have to ‘bribe’ informed employees to secure their
commitment to cartel agreements. They point out that a colluding firm would have to compensate employees for the legal risk to which they are exposed. Therefore, both corporate and individual leniency programs are considered to be more effective due to decreasing benefits of collusion. My analysis builds upon this insight and takes into account the compensation to informed employees by risking individual fines or prosecution. Finally, in the last part of their paper they briefly discuss the possibility of individual rewards creating or exacerbating agency problems between owners and employees.
A paper that examines this abrasive interaction and takes into account the corporate governance issues due to individual liability, is the paper of Th´epot (2011). Without individual sanctions, cartel detection leads to administrative or monetary fines that are born by a firm as a whole.
Shareholders bear most sanctions while managers may avoid direct punishment for their actions completely. Also, managers may have left the company by the time that a company’s cartel involvement is detected. Th´epot (2011) argues upon three parameters that determine managerial cartel involvement: the expected profits, the expected cost of detection (i.e. sanction) and the probability of being detected (Th´epot, 2011). Besides managerial involvement, a principal (owner) in not always an innocent victim of an agent’s crime. Owners are likely to gain from cartel agreements, since a firm benefits as a whole once cartel agreements lead to increased profits.
For my model it is important to distinguish these different cartel involvements and look at the role of principles, agents, shareholders and employees. One possible explanation for illegal cartel involvement, is a misalignment between corporate governance. Due to limited observability of an agent’s action by a principal (asymmetric information), moral hazard problems1 can lead to collusive behavior since an agent does not bear the full costs of his actions. However, corporate governance issues could also induce shareholders to provide an agent with the incentive to engage in cartel agreements (Th´epot, 2011).
To strengthen my model it is important to classify individual sanctions and argue on whom these sanction will be levied. Based on the article of Th´epot (2011), efficiency of antitrust enforcement is believed to increase by sanctioning managers and employees. Individual sanctions would be useful to align incentives between the principal and the agent and decrease moral hazard problems in cartel participation. Managers incentives to misbehave are reduced due to the fear of personal conviction. However, arguments against individual sanctions should also be considered. Spagnolo (2006) argues that sanctioning managers may not be a relevant instrument since it does not take away the incentive for shareholders to take part in a cartel. Depending on the corporate governance
1Moral hazard problems: opportunistic behavior that is likely to arise between a principal and agent due to asymmetric information and the agent’s incentive not to act in the best interest of the principal. (Roberts, 2004)
system, individual liability as an enforcement instrument has its pros and cons. According to Th´epot (2011), individual sanctions are however desired due to the limited liability regime and the probable inability of firms to pay high fines. Nevertheless, Th´epot (2011) also admits that individual sanctions may not be directly deterrent for an owner and that the impact of these sanctions in leniency programs may be limited. In the case of separate ownership and control, individual leniency would be more efficient and increase the cost of collusion, including improved incentives towards a better market conduct.
4.1 Why individual penalties?
It is clear that individual penalties can provide a solution to the problem of corporate sanctions being unable to bring about effective deterrence. Individual sanctions especially strengthen the moral commitment to law and should therefore be used in combination with corporate penalties.
According to Wils (2002), exclusive reliance on on corporate sanctions make deterrence unattain- able for most Antitrust Authorities. Effective deterrence would imply impossibly high fines and the fines would mostly exceed the undertakings’ ability to pay. Also, corporate sanctions do no often provide sufficient incentives for responsible individual behaviour. By combining both corpo- rate and individual liability, the need for very high corporate sanctions can be reduced. However, increasing deterrence by individual penalties can be inefficient by the limited individual ability to pay. The use op imprisonment as a credible threat could help to overcome this limitation.
Another argument in favor of individual sanctions is linked to the limited ability of firms impos- ing sanctions on their employees due to high cost of intensive monitoring. Every firm avoiding antitrust violations should therefore be willing to accept this individual liability of their employees.
Throughout this paper I consider both corporate and individual fines as a combination in compe- tition policies. According to Wils (2002), there are several reasons for individual fines only being effective in combination with corporate fines. In absence of corporate sanctions, firms would could encourage their agents into collusive behavior whereas corporate liability stimulates firms to con- trol their agents’ misconduct. Another reason relates to minimizing enforcement costs, since both the firm and individual defendants can be prosecuted on the basis of the same evidence. Finally, a combination of both penalties increase the potential of plea bargaining, since most defendants will have the incentive to reveal each others’ involvement in return for immunity or a fine reduction.
In essence, loyalty to the firm becomes less beneficial compared to a reduction in fines.
5 The Model
5.1 Antitrust enforcement
In section 5, I will examine the probability of cartel detection as well as the enforcement choices of the Antitrust Authorities. The paper of Chen and Rey (2012) is used to form the basis of my model. This model is based on a duopolistic Bertrand model, where firms simultaneously choose to compete or collude.2
5.1.1 Probability of detection
Most competition policies have increased the probability of detecting a cartel. Due to a lack of resources within the antitrust divisions, not all cartels are actually discovered. Therefore, it is important to include such probabilities into the model to argue on the cartel stability once the probability of detection increases. I assume that cartels leave some evidence, which an Antitrust Authority can find once it opens an investigation. The probability of cartel detection will be divided into the launch of an investigation and its outcome. More precisely, I will include the following parameters:
• In the absence of any report, the Antitrust Authority will open an investigation with prob- ability α, where 0 < α < 1
• In the absence of any report, if the Antitrust Authority has already launched an investigation, it succeeds in uncovering a cartel with probability ρ, where 0 < ρ < 1
In practice, both α and ρ are expected to be quite small, due to limited resources and fundamental difficulties in uncovering hidden evidence (Chen and Rey, 2012). If the antitrust authority is not able to detect a cartel, the probability of detection will be equal to zero. In the case of limited budgets, leniency programs can help to increase this probability of detection. If an investigation is opened and at least one firm cooperates, the other cartel members will be convicted with probability one.
5.1.2 Enfrocement choices
Once an antitrust authority succeeds in uncovering a cartel, they can impose a fine F ∈ (0, ¯F ) for the firms that are considered guilty. The maximum fine ¯F is different per country and is exogenously given by law. To simplify the model, it is assumed that evidence of collusion is
2See Appendix A for the collusive game
generated if both firms agree on collusion. Furthermore, cartel agreements only last one period.
After each period both firms have to decide whether to continue their collusive agreements. This implies that a cartel cannot be prosecuted for its past activity and can only be fined for the current period.
To include leniency programs into the model, I assume an informant to benefit from a reduced fine equal to (1 − q)F , where 0 < q ≤ 1. If the antitrust authority chooses to grant the first applicant with full immunity of any fines, q will be set to one.
5.2 Collusive strategies
There are different strategy profiles of the firms that should be considered. In an infinitely repeated game there are three simple collusive strategies:
• CR: Collude and Reveal. Firms will collude as long as no deviation occurs. If the Antitrust Authority does not open an investigation, both firms agree to collude on the market and set a monopoly price. Once an investigation has been opened, firms will provide evidence to the Antitrust Authority and pay a reduced fine or get full immunity from any sanctions. If a deviation occurs either in the market place or by revealing a cartel, each firm will set a competitive price forever onward.
• CNR: Collude and Not Reveal. Firms will collude as long as no deviation occurs. If the Antitrust Authority does not open an investigation, both firms agree to collude on the market and set a monopoly price. Once an investigation has been opened, firms will not provide any evidence to the Antitrust Authority. If firms are proved guilty, they pay a full fine and are forced to set competitive prices forever onward. Also, if deviation occurs from any agreement, firms will set competitive prices forever onward.
• NC: No Collusion. Each firm will set competitive prices every period.
It is important to note that deviations from these strategies can be twofold. First, a firm can deviate on the market by setting a price just below the monopoly price. Second, if the Antitrust Authority opens an investigation, firms can deviate by reporting the cartel. In both cases, firms will return to set competitive prices and obtain πN = 0, for every future period.
5.3 Timing of the game
Under the assumption of firms playing an infinitely repeated game where they compete in prices and supply homogeneous products, firms have to make several decisions each period. The timing
of this game is as follows:
• Stage 1. Each firm chooses whether to enter into any collusive agreements, i.e. establish a cartel. If one firm chooses not to collude, the game ends for that period.
• Stage 2. If the firms collude, they set a collusive strategy and choose whether to adhere to the agreements or to deviate and compete on the market. These decisions are not observed by rivals until the end of the period; then:
• Stage 3. First the Antitrust Authority opens an investigation with probability α ∈ (0, 1), into any collusive agreements amongst the firms. The assumption is made that firms observe this decision. Next, firms choose whether or not to report the cartel. There are four situations that can occur:
First, once an investigation has been opened and neither firm chooses to report the cartel, the Antitrust Authority uncovers the cartel with probability ρ ∈ (0, 1). If this is the case, both firms pay a full fine F . Second, if an investigation has been opened and at least one firm reports the cartel, the cartel in uncovered with certainty. The reporting firm pays a reduced fine (1 − qa)F , while the other firm pays the full fine F . If both firms apply for leniency, each firm is the first one to report with probability 0.5 and pays the reduced fine, whereas each firm is second with probability 0.5 an pays the full fine. Third, if neither firm chooses to report the cartel and there is no investigation being opened, the cartel will not be convicted. Fourth, if no investigation has been opened and one firm chooses to report the cartel, the cartel is uncovered with certainty. The reporting cartel pays a reduced fine (1 − qb)F and the other firm pays the full fine F . When both firms apply for leniency, each firm pays a reduced fine with probability 0.5, whereas each firm is second with probability 0.5 an pays the full fine.
5.4 Critical discount factor without leniency
In the absence of a leniency program, deviating to denounce a cartel will not be beneficial for each firm. Cartel members will have monopoly profits before detection. However, both firms should take into account the probability of detection and the possible fine once a prosecution is successful. Therefore, each period brings a net profit πC, minus the expected fine αρF . The expected discounted value of normal collusion will therefore be equal to:
VC =πC− αρF 1 − δ
The discounted value of deviating will be equal to:
VD= πD− αρF + δ 0 1 − δ
In order for collusion to be sustainable, profits from collusion should be higher than the profits from deviating considering the probability of a possible fine (VC ≥ VD). This means that for collusion to be sustainable, the critical discount factor is equal to:3
δ∗≥ πD− πC
πD− αρF (1)
Compared to equation (14), equation (1) shows that the critical discount factor at which collusion is sustained is increased if sanctions are included in competition policies. This is due to a reducing factor in the denominator. Collusion is therefore less sustainable with the possibility of fines, since collusion is now stable for a smaller set of deltas. Also, collusion is now less sustainable since profits should be sufficiently higher than the cost of detection. The effectiveness of this antitrust enforcement is increased by either and increasing probability of detection αρ and/or an increased fine F .
5.5 Individual sanctions
In section 5.5, I will examine the effect of individual liability, which turns out to have a destabilising effect on cartel agreements. Cartel agreements often rely on the involvement of several people from different companies. The Antitrust Authority can take advantage of this, since these agreements often create agency problems. In particular, misalignment between principals and agents and moral hazard problems can be resolved by individual sanctions. To include these sanctions into my model, I will consider a compensation towards agents and/or employees for the risk of individual liability.
Colluding firms are considered to ‘bribe’ agents and informed employees to secure their fidelity.
As a results, benefits from collusion will decrease. Therefore, individual sanctions will most likely make collusion less stable.
The approach of individual compensation as a cost to the firms should take into account the liability and the number of individuals involved. Not every individual is equally important and will be equally punished once a cartel is uncovered. Also, larger compensations could be required once local competition policies allow for imprisonment compared to monetary fines. The total profit decreasing amount of compensation given by the firm will therefore be the sum of compensating
3See Appendix B for proof (1) and (2)
returns R, times an individual liability measure βi, with βi ∈ (0, 1). The maximum level of individual liability will act as a benchmark for individual compensation, after which the total amount of profit reduction will depend on individual involvement. By including this to the initial model, collusion will only be sustainable if:
πC− αρ(F +Pn i=1βiR)
1 − δ ≥ πD− αρ F +
! + δ 0
1 − δ
The critical discount factor including both corporate and individual fines above which collusion is now sustainable, is equal to:
δI ≥ πD− πC πD− αρ(F +Pn
By comparing equation (1) and (2), it could be argued that individual sanction increase the effectiveness of antitrust enforcement since δI > δ∗. Due to a further decreasing effect of individual liability in the denominator, collusion will be sustainable for a smaller set of deltas. Also, a higher discount factor decreases the net present value of a cartel, increasing the opportunity cost of deviating. Therefore, in absence of any leniency, including both corporate and individual fines to the model increases the destabilizing effect of antitrust enforcement.
An alternative way of looking at the effectiveness of antitrust enforcement is to calculate the threshold level of colluding profits that stabilizes cartel agreements. This can be done by solving the cartel stability condition in terms of profits:4
πC ≥ πIC= δαρ
2δ − 1 F +
From equation (3) it can also be seen that antitrust enforcement becomes more successful by including both corporate and individual sanctions. The probability of detection αρ, fine level F and the number of involved individualsPn
i=1βiR, increase the threshold level of colluding profits πCI .
5.6 Collusive strategies under leniency
In section 5.6, leniency programs are introduced which gives the informant(s) a fine reduction if they provide sufficient evidence on the cartel. I will consider the possibility of both amnesty
4See Appendix C for proof equation (3)
given before and after an investigation has been opened, like the Antitrust Divisions’ Type A/B leniency. It turns out that the effectiveness of granting amnesty after an investigation depends on different collusive strategies. However, introducing leniency programs is optimal when the overall probability of conviction is small.
Also, the optimal amnesty rate should deter cartels such that the profits from collusion are smaller than the expected threshold level of collusive profits under a leniency program:
πLC(αρ) > πC
Based on my analysis, there are some differences concerning the availability of amnesty rewards.
Some countries only rewards amnesty to the first applicant, whereas other countries also reward a second and a third applicant with a reduces fines. To simplify the model I assume that any fine reduction will only be granted to the first applicant. To model the difference between the timing of a report, qb and qa respectively denote the reduced fine offered to the informant that reports the cartel before and after an investigation has been launched. The following sections will examine four types of collusive strategies under leniency programs and individual sanctions. The first two strategies only includes amnesty before an investigation has been opened and the final two strategies consider both amnesty before and after an investigation has been opened.
5.6.1 Amnesty before investigation
The first collusive strategy to be considered is ’Collude and Not Reveal’, where firms choose to collude as long as no deviation occurs. The value of collusion will be equal to a situation without leniency. However, a deviating firm can now report a cartel and benefit from leniency. Firms will have the incentive to do so if the amnesty rate reduces the expected fine they face. Therefore, the probability cartel detection αρ is set to one, for the expected fine reduction of the deviating firm.
Additionally, the assumption is made that once a firm applies for leniency, individuals within a cartel can expect the same level of corporate fine reduction5. Therefore, the compensating returns Pn
i=1βiR will also be reduced by (1 − qb). ’Collude and Not Reveal’ will now only be sustainable when the following cartel stability condition holds:
5https://uk.practicallaw.thomsonreuters.com, overview of country specific leniency application schemes, where most countries consider both individual and corporate fine reductions after leniency application
VN R=πC− αρ(F +Pn i=1βiR)
1 − δ ≥ πD− (1 − qb) F +
The value from deviating will be increased since the possible fines are reduced by (1 − qb). This collusive strategy with both leniency and individual fines is only sustainable when colluding profits are above the threshold level:6
πC≥ πN RC (qb) =αρ − (1 − δ)(1 − qb)
2δ − 1 F +
The threshold level of cartel profits πCN R(qb) can be calculated by solving the cartel stability condition in terms of profits and it increases with the amnesty rate given to a firm. Under the strategy of ‘Collude and Not Reveal’ , both individual fines and leniency give the firms an extra incentive to report the cartel to the Antitrust Authority since it becomes harder to sustain collusive agreements once the threshold level of stable cartel profits increases. Additionally, under this strategies, leniency should be preferred to a policy without leniency if the following condition holds:7
qb> qb= 1 − αρ > 0 (5)
When this condition holds, the threshold level of cartel profits (4) are higher than the threshold level of cartel profits (3) without leniency. Therefore, if the effective probability of cartel prosecu- tion ’αρ’ is small, leniency should be sufficiently high to efficiently destabilize or prevent any cartel agreements.
Alternatively, firms can ’Collude and reveal’ once an investigation has been launched. However, if an Antitrust Authority does not give amnesty after an investigation has been launched, this strategy results in the same outcome as ’Collude and Not reveal’. Nevertheless, firms can choose to systematically ‘Collude and Reveal’. They could collude and make agreements on the applica- tion to leniency. Due to a lack of resources within the Antitrust Authority, cartel members can again collude and apply for leniency after the first firm has applied. This exploitation of a leniency program enables firms to receive most benefits out of collusion and report the cartel before an investigation has been opened. When both firms adhere to this strategy, they are equally likely to be the first applicant. Also, if both firms agreed to collude and reveal, the first applicant pays half of the fine to the other firm to compensate the costs. This form of collusion is sustainable as long as firm have no incentive to deviate and compete on the market. If one firm does deviate, it
6See Appendix D for proof (4)
7See Appendix E for proof (5)
becomes optimal for both firms to apply for leniency. Assuming they are equally likely to be the first informant, the cartel stability condition is given by:
VR= πC− (1 −q2b)(F +Pn i=1βiR)
1 − δ ≥ πD− (1 −qb 2) F +
In this stability condition, the effective probability of prosecution ’αρ’ is set to one since both firms agree to report the cartel before an investigation has been launched. Both collusive and deviating profits are now only being reduced by half the amnesty rate before an investigation given to the first applicant (1 −q2b), due to compensating costs to the other firm. The threshold level of profits is therefore given by:8
πC≥ πRC(qb) =δ(1 − q2b) 2δ − 1 F +
(6) Again, the threshold level πCR(qb) can be calculated by solving the stability condition in terms of profits. These colluding profits now decreases as the amnesty rate before an investigation ’qb’ increases. Offering additional leniency makes this form of collusion more attractive. Yet, individual liability makes this form of collusion less attractive due to an increasing level of stable cartel profits.
However, under this strategy, leniency should be preferred to a policy without leniency when:9
qb> ¯qb= 2(1 − αρ) > 0 (7)
When this condition holds, the cartel profits (6) are higher then the threshold level of cartel profits (3) without leniency. Therefore, under this condition, this alternative collusive strategy is more robust than normal collusion without leniency.
The exploitation of a leniency program with both firms systematically colluding and revealing can be prevented by the Antitrust Authority. Assuming that the Antitrust Authority does not want this exploitation, condition (5) and (7) can be used to argue upon the optimal amnesty rate given to the first applicant before the launch of an investigation. The optimal amnesty rate before the launch of an investigation ’qb’, should therefore be within the range:
1 − αρ < qb< 2(1 − αρ)
When qbis higher that 1 − αρ firms will have the incentive to apply for leniency. When qbis smaller than 2(1 − αρ), exploitation of a leniency program will not be sustainable.
8See Appendix D for proof (6)
9See Appendix E for proof (7)
5.6.2 Amnesty before and after investigation
This section tries to analyse the effectiveness of offering leniency before and after an investigation has been opened. Similar to the previous section, I will consider two collusive strategies. The first collusive strategy to be considered is ’Collude and Not Reveal’. Each period firms have collusive profits. Once the Antitrust Authority opens an investigation, both firm choose not to report the cartel. One firm can choose to deviate from the cartel agreements and will have the incentive to report the cartel. However, deviating profits after leniency will now depend on the probability that an investigation is being opened ’α’, since the Antitrust Authority offers different fine reductions before and after the opening of an investigation. Once again, the assumption is made that individuals within a cartel are offered the same fine reduction as the company. ‘Collude and Not Reveal’ will now only be sustainable if the following condition holds:
VN R= πC− αρ(F +Pn i=1βiR)
1 − δ ≥ πD− [(1 − α)(1 − qb) + α(1 − qa)] F +
Profits from collusion will not differ from collusive profits in the previous section. However, de- viating profits will now depend on the probability of receiving amnesty before an investigation (1 − α)(1 − qb) and on the probability of amnesty given after the launch of an investigation α(1 − qa). This collusive strategy with both leniency and individual fines is only sustainable when colluding profits are above the threshold level:10
πC≥ πN RC (qb, qa) =αρ − (1 − δ)(1 − (1 − α)qb− αqa)
2δ − 1 F +
This threshold level of colluding profits can be calculated by solving the stability condition in terms of profits. If the amnesty rate before and after an investigation increases, the threshold level of cartel profits πCN R(qb, qa) will also increase since both ’qb’ and ’qa’ have an increasing effect in the numerator. Hence, under the strategy ‘Collude and Not Reveal’ both individual fines and leniency increase the incentive to deviate from cartel agreements. Additionally, a higher level of fine reduction after opening an investigation may be preferred if the probability of opening an investigation ’α’ increases. Therefore, leniency before and after an investigation should be preferred to a policy with only leniency before an investigation if the following conditions holds:11
qb < qa (9)
10See Appendix F for proof (8)
11See Appendix G for proof (9)
Once his condition holds, the threshold level of cartel profits (8) are higher then under the thresh- old level in proposition (4). Since both firms agreed on not reporting the cartel, the Antitrust Authority can only further destabilise these agreements by increasing the amnesty rate after an investigation is launched.
Alternatively, firm can now choose to report collusion to benefit from a reduced fine once an investigation has been launched. Again, firms could systematically ‘’Collude and Reveal’ which would result in the same threshold level of profits (6). The best response for both firms is to report since other firms will report anyway.
However, if firms do not choose to ‘Collude and Reveal’ systematically, they can now report a cartel once an investigation has been launched. If both firms have this strategy, reporting in case of an investigation becomes self-sustainable, irrespective of whether the other firm deviates. Given that the other firm will report the cartel, reporting becomes optimal since it reduces the expected fine by half a chance of receiving any fines reduction after the launch of an investigation (1 − qa/2).
Therefore, this collusive strategy is only sustainable for two types of deviations. One in which a firm deviates and reports the cartel in stage 2 and one in which a firm deviates in case of investi- gation.
In stage 2, firms will have no incentive to deviate if:
VR=πC− α(1 −q2a)(F +Pn i=1βiR)
1 − δ ≥ πD− (1 − qb) F +
Colluding profits now depend on the probability of deviating after the opening of an investigating and receiving a reduction in fines with a probability of one half given by α(1 −q2a). Also, deviating profits are assumed to depend on reporting the cartel before an investigation and receiving a fine reduction equal to (1 − qb). This collusive strategy with both leniency and individual fines is only sustainable when colluding profits are above the threshold level:12
πC≥ πRC(qb, qa) =α(1 −q2a) − (1 − δ)(1 − qb)
2δ − 1 F +
Again, this threshold level of colluding profits can be calculated by solving the stability condition in terms of profits. The threshold level of profits πCR(qb, qa) now increases as the amnesty rate before investigation increases. However, the possibility of offering amnesty after an investigation tends to decrease the threshold level of cartel profits, making collusion more sustainable. Firms find it more easy to adhere collusive agreements once they know that they get a possible fine reduction
12See Appendix F for proof (10)
if they would reveal the cartel once an investigation has been opened. Due to their strategy of
’collude and reveal’ once an investigation has been opened, an increased amnesty rate after the opening of an investigation creates less incentive to deviate and report a cartel on beforehand.
Considering a deviation after an investigation has been launched, firms will have no incentive to deviate if:
VR= πC− α(1 −q2a)(F +Pn i=1βiR)
1 − δ ≥ πD− α(1 −qa 2) F +
Under this strategy, deviating profits will depend on the probability of receiving a fine reduction α(1 −q2a). This collusive strategy with both leniency and individual fines is again only sustainable when colluding profits are above the threshold level:13
πC≥ πCR(qa) =δα(1 − q2a) 2δ − 1 F +
The threshold level of profits πRC(qa) now again decreases for a higher amnesty rate after an inves- tigation has been launched. Again, colluding firms will find it easier to sustain colluding agreement under this strategy when this amnesty rate increases. Yet, offering leniency during an investigation will further destabilize a cartel once an investigation has been launched. Especially if an investi- gation is likely to succeed without cooperation, qa > 0 may encourage firms to collude and report in case of investigation. If the Antitrust Authority is willing adopt post investigation leniency and destabilize normal collusion by stimulating deviate and report in case of an investigation, the following condition should be met:14
α(1 − qa) < 1 − qb (12)
Under this condition, colluding firms are more likely to deviate and report in absence of an inves- tigation since the threshold level of profits for deviating and reporting is case of an investigation are higher than he threshold level of profits for deviating only before the launch of an investigation [πRC(qa) > πCR(qb, qa)].
Alternatively, an effective policy could give firms a disincentive to collude ”but” report in case of an investigation. In that case, the following condition should be met:15
qa< 2(1 − p) (13)
13See Appendix F for proof (11)
14See Appendix H for proof (12)
15See Appendix I for proof (13)
Under this condition, the threshold level of profits for deviating in case of an investigation are higher than under the threshold level of profits where firms are more tempted to deviate and re- port before an investigation [πCR(qb, qa) > πCN R(qb)]. Therefore, firms will have less incentive to wait and report a cartel if an investigation has been launched.
Offering leniency before an investigation can be an effective tool, especially if there is a low prob- ability of detection. Offering leniency after an investigation can also be effective especially if the investigation is likely to succeed without cooperation. Depending on different colluding strategies, offering leniency can form an effective tool to destabilize cartels. In addition, independent of any collusive strategies, a combination of corporate and individual liability both have a large desta- bilizing effect, since they decreases collusive profits. Also, firms will be more likely to apply for leniency once they face a higher charges.
5.7 Individual leniency
Besides individual liability, some jurisdictions also adopted individual leniency as an effective policy tool. Section 5.7 examines this tool in a game theoretical way taking into consideration a corporate governance structure, where top managers are assumed to have more incentive to apply for corporate leniency in stead of individual leniency.
5.7.1 Top/Middle managers
According to the paper of Spagnolo (2008), decisions from cartel agreements are typically made by top level managers that issue these decisions to lower level managers that try to hide collusive agreements. Therefore, middle managers are assumed to provide less information to the Antitrust Authority if they would apply for individual leniency. To argue on the incentives of both top/middle managers, it is important to distinguish their payoff schemes from any cartel agreements. In essence, top managers are likely to be discouraged from individual defection when firms have agreed upon collusion. In most cartel cases, top managers receive stock options in the firm as part of their collusive benefits. Apart from more commitment to the cartel, top manager will be less likely to only apply for individual leniency due to this stock-based incentives.
However, due tot the limited corporate liability of middle managers, individual leniency programs are assumed to increase deterrence due to higher agency cost of collusion and increasing governance problems of firms involved in a cartel (Spagnolo, 2008). Furthermore, individual leniency is unlikely to be used, but it forms a credible threat in the hands of individual whistleblowers as it pushed top
managers to apply for corporate leniency before middle managers apply individually. In addition, the threat of individual liability will tend to further increase these whistleblowing incentives. In the following section I model this interplay between top and middle managers and find an equilibrium that is in line with former predictions.
5.7.2 The individual leniency game
Before arguing on the credible threat of individual leniency policies, I consider several assumptions in this simultaneously played game. Due to the issuing of decisions of top managers on middle managers, the assumption is made that middle managers only provide information that is sufficient to open an investigation. Whereas top managers are assumed to have perfect information on any collusive agreements. Considering the additional benefits that both manager receive during a cartel, top managers are assumed to receive part of their benefits in stock options or shares in the firm. A top manager will therefore always apply for corporate leniency in stead of an individual leniency application. Also, according to most competition policies, both the company and individuals get a full fine reduction after a corporate leniency application.
Under the assumption of top/middle managers playing an one shot game, individuals will balance the costs and benefits of continuing their illegal activity. Within jurisdictions where imprisonment is part of individual sanction, the incentives to blow the whistle will be strong. In term of my game theoretical model, individual leniency makes the managers dilemma even more complex since it effects a two-dimensional system: a horizontal one between cartel members, and a vertical one between individuals within the firm. The timing of this game is as follows:
• Stage 1. Each firm chooses to enter into collusive agreements, i.e. establish a cartel. If one firm chooses not to collude, the game ends for that period.
• Stage 2. If both firms collude, there are two possible deviations for the managers involved in the cartel. First, a middle manager can either choose to continue the cartel, or choose to apply for individual leniency. Second, a top manager can choose to continue the cartel, or choose to apply for corporate leniency.
• Stage 3. Under the assumption of corporate leniency also applying on individuals, a middle manager obtains a reduction in fines once a top manager applies for corporate leniency. If only the middle manager applies for individual leniency, due to limited information, a top manager will face a fine with the probability of the Antitrust Authority uncovering the cartel
’ρ’. Also, due to a two-dimensional system, the probabilities of receiving a reduction in fines