This article proposes a new approach to measuring the deterrent effect of cartel law enforcement by combining a game-theoretic model with Monte Carlo simulations. The game-theoretical analysis shows which type of perfect Bayesian Nash equilibria is obtained depending on the parameter setup: perfect compliance, imperfect compliance or zero compliance. For each equilibrium, we also derive the probabilities of type I (false-positive) and type II (false-negative) errors committed by the cartel authority. To account for the uncertainty and the vague knowledge concerning the model parameters, we perform Monte Carlo simulations based on parameter ranges extracted from the related literature. The simulations indicate that zero compliance dominates the picture and that the error probabilities are high for type II and negligible for type I errors. The results are fairly robust against correlation in the input parameters. Further robustness studies and interactive visualizations can be obtained with a supplemental web application.
We are indebted for helpful comments and suggestions to Andrea Günster, Ronald Heiner, Jenny Helstroffer, Roland Kirstein, Stefan Klößner, Christian Koboldt, Christian Pierdzioch, Maarten Pieter Schinkel, Edmund Schuster, Stefan Voigt, Ansgar Wohlschlegel, Wouter Wils and Daniel Zimmer for helpful comments. We also thank two anonymous referees for their very valuable suggestions which improved the presentation considerably.
In this case, F perfectly complies with the competition law by choosing a compliance level , i. e. signing a legal (good) agreement with certainty, and the Commission never prohibits a controlled agreement regardless of the received signal (). Consistently, the posterior beliefs and also amount to 1, i. e. the Commission knows for certain that it has reached the decision nodes and , respectively, which is only possible if the firm chooses to form an exempted (legal) agreement.
The second row of Table 1 describes the possible equilibria in parameter constellation PC 2. The equilibrium set EQS 2.1 is reached if the condition , i. e. , holds. In this case, an infinite number of equilibria exists:
In every equilibrium out of this set F chooses a legal agreement with probability , while the Commission again never prohibits an agreement regardless of the received signal (). The corresponding posterior beliefs depend on F’s choice and range from to for and from to for . In addition to this, a second set of equilibria exists in parameter constellation PC2:
Here, the firm chooses a compliance level and the Commission prohibits every agreement with certainty regardless of the received signal (). The corresponding posterior beliefs again depend on the firm’s choice of agreement and range from to for and from to for .
In the third row of Table 1, the equilibria for the parameter constellation PC3 are depicted. If the condition , i. e. , holds, three different equilibria can be realized:
In equilibrium EQ 3.1, the firm chooses to form a legal agreement with probability . This agreement is exempted from the cartel ban with certainty if the signal is i = l () and with probability if the signal is i = ill. The corresponding posterior beliefs amount to . In equilibrium EQ 3.2, the firm’s compliance level is smaller: . The Commission reacts to this behavior by prohibiting the agreement with certainty whenever the signal is i = ill () and by not objecting to it only with probability whenever the signal is i = l. This decision is based on the equilibrium posterior beliefs . Finally, equilibrium EQ 3.3 is characterized by zero compliance of the firm () and an unconditional ban decision by the Commission (). Consistently, the Commission’s posterior beliefs that it has reached decision node or , which is the case when the firm has set up a legal agreement, also equal zero ().
If the condition , i. e. (PC4), is fulfilled, there again exist multiple equilibria, namely the equilibrium set EQS 4.1 and the equilibrium EQ 4.2 already known from parameter constellation PC3. EQS 4.1 is defined as follows:
Each of these equilibria implies the firm choosing to form a legal agreement with probability and the Commission prohibiting the agreement whenever the signal is i = ill) and not objecting to it whenever the signal is i = l (). The corresponding posterior beliefs range from to for and from to for .
Finally, in the fifth row of Table 1, the equilibrium of parameter constellation PC5 is depicted. If the condition , i. e. , holds, equilibrium EQ5 – already known from parameter constellations PC3 and PC4 – is realized.
B (Equilibrium Selection)
Let us first consider parameter constellation PC2. Here we face a twofold equilibrium selection problem: (1) There are two sets of equilibria EQS 2.1 and EQS 2.2. (2) Within these sets of equilibria, there exist an infinite number of equilibria which differ only with respect to the firm’s compliance level while the Commission’s action remains unchanged. It is worthwhile noting that the multiple equilibria within one set have an interesting feature: they all lead to the same payoff for the firm irrespective the concrete value taken by F’s behavioral strategy . In the equilibrium set EQS 2.1, this payoff amounts to , in EQS 2.2 to . Thus, the firm is indifferent with respect to its actual compliance level within the given range. In other words, the firm does not prefer a specific equilibrium within EQS 2.1 and EQS 2.2. It is therefore possible to make the following assumption: Whenever the firm is indifferent regarding its compliance level, it choses the highest possible compliance level as it does not face any opportunity cost in doing so. Consequently, the equilibrium sets EQS 2.1 and EQS 2.2 can be reduced to two single unambiguous equilibria: In EQS 2.1, the firm chooses so that EQ 1 is reached given the Commission’s equilibrium strategy and its equilibrium posterior beliefs ; in EQS 2.2 the firm chooses , while the Commission chooses based on its posterior beliefs . This latter equilibrium is a special case of equilibrium EQ 3.2 in parameter constellation PC3 (): it is the limit of EQ 3.2 for to (yielding ) while is the defining criterion for parameter constellation PC2.
Let us now turn to the second problem in this parameter constellation. Reducing the equilibrium sets EQS 2.1 and EQS 2.2 to one equilibrium each does not fully solve the equilibrium selection problem; there still exist two equilibria in parameter constellation PC2, namely EQ 1 and EQ 3.2. Which of those will be realized? Both equilibria are consistent combinations of equilibrium strategies and corresponding beliefs and therefore are both equally feasible. Still, EQ 1 features a focal point quality which EQ 3.2 does not. The firm’s payoff is higher in EQ 1 than in EQ 3.2. To resolve the selection problem, we refer to a concept known as virtual observability. In our model, the firm is a first-mover as its “real life” move lies before the Commission’s choice, but due to imperfect information the Commission cannot observe the firm’s choice – a situation which is typical of simultaneous games. However, the Commission can anticipate this behavior assuming that the firm will try to reach an equilibrium that maximizes its expected payoff. Thus, the second-mover acts as if the moves of the first-mover were observable. This kind of equilibrium selection is not only intuitively reasonable, but numerous experiments have also provided evidence for it. Hence, the multiple equilibria in parameter constellation PC2 can be reduced to one single equilibrium, namely EQ 1.
In parameter constellation PC3, three different equilibria exist, namely EQ 3.1, EQ 3.2 and EQ 3.3. The concept of virtual observability can again be applied as the firm’s payoff in EQ 3.1 is higher than the ones realized in EQ 3.2 and EQ 3.3. Thus, equilibrium EQ 3.1 dominates the other two equilibria.
In parameter constellation PC4, the equilibrium set EQS 4.1 and the equilibrium EQ 4.2 exist. Within EQS 4.1, the firm’s expected payoff amounts to a single value regardless of the compliance level chosen, namely . Hence, following the same reasoning as above, it can be assumed that the firm chooses the highest compliance level feasible, i. e. . This equilibrium is a special case of equilibrium EQ 3.1 in parameter constellation PC3 (): it is the limit of EQ 3.1 for to (yielding ), while is the constituting condition for parameter constellation PC4.
Control probability (detection probability)
The following estimates can be found in the literature: 10 % (Werden and Simon 1987), 13–17 % (Bryant and Eckard 1991; sample of cartels indicted in the United States between 1961 and 1988). Combe, Monnier, and Legal (2008), applying the same methodology as Bryant and Eckard, calculate a probability of detection in a given year lying between 12.9 % and 13.2 % (sample of all cartels convicted by the European Union between 1969 and 2007). In a recent study, Combe and Monnier propose to use a detection probability of 15 % (Combe and Monnier 2009: 19). This probability is also assumed in the simulation run by Buccirossi and Spagnolo (2007). According to Connor and Bolotova (2006: 9), most evidence seems to suggest a probability between 10 % and 20 %.Connor and Lande (2012) – reviewing the relevant literature – report the following figures: 20.8 %–27.2 % (quantitative economic studies) and 25.6 % (opinions of cartel scholars). Opinion surveys deliver “non-quantifiable but low estimates that are roughly consistent with the first two estimates” (Connor and Lande 2012: 465). Ormosi, applying a method commonly referred to as capture–recapture model or mark and recapture analysis, which is widely used for population studies in ecology, finds that less than a fifth of cartels have been detected in the EU between 1985 and 2005 (Ormosi 2014: 565).
As the number of cartels remaining undetected is unknown, the probabilities of detection are only vague estimates. Moreover, what actually matters is the subjective probability of a cartel getting caught. Note that the detection of a cartel does not necessarily lead to an infliction of fines. Therefore, the detection probability should be discounted by the conviction rate. Using a conviction rate of 75 % would lead to a probability of being fined of 7.5–15 %. Private enforcement as well as the leniency program might increase this range to 11.25–18.75 %. We run a simulation for the control probability range [5 %,30 %].
Camesasca et al. (2013) consider a sample of 510 parties fined in the period 1998–2009 directed against fines, procedure, facts and substantive assessment: only 29 parties had their fine annulled by the GC) and 2 had it annulled by the CJ; in 104 and 65 cases the GC and the CJ, respectively, upheld the fine and dismissed the case. The remaining parties are still awaiting a judgment or had their appeals removed (Camesasca et al. 2013: 217). Overall, from 1081 pleas that have been filed (against fines, procedure, facts and substantive assessment), only 94 have been successful (Camesasca et al. 2013: 217), which gives a success rate of about 9 %. This is also the overall success rate of pleas directed against fines. The authors conclude: “Regarding the overall success rate, our findings confirm common knowledge – that Commission decisions are upheld on appeal, save for rare exceptions” (Camesasca et al. 2013: 217).
Harding and Gibbs (2005: 365) share this view in principle. From 200 appeals (1995–2004), 6 % are – formally – categorized as successful, 61 % as partly successful (fine reduction) and 33 % as unsuccessful. But they add that a closer reading of the cases termed “partly successful” might suggest that this category should be renamed “largely unsuccessful” (Harding and Gibbs 2005: 366).
Hüschelrath and Smuda (2014) use data of 467 firm groups in 88 cartels convicted by the European Commission between 2000 and 2012: 50 % decided to file an appeal, with 47 % being successful in the sense of receiving a reduction in the fine originally imposed by the Commission (Hüschelrath and Smuda 2014: 17–18). These figures imply that about 25 % of the firm groups successfully appealed and received a fine reduction. But again – as mentioned above – some cases might better be termed “largely unsuccessful”.
Smuda, Bougette, and Hüschelrath (2014) use data of 234 firm groups that participated in 63 cartels convicted by the European Commission between 2000 and 2012. They find that in sum 109 of the 325, i. e. 34 %, first-stage appeals were successful, whereas only 5 % were successful in second-stage appeals.
According to the divergent results of the studies presented above, it seems reasonable to assume in our simulations a reversal rate ranging from 10 to 40%.
Since we are not aware of any estimates of the profitrate associated with legal agreements, we refer to the competitive markup (competitive price–cost margin) used in the literature on the deterrent effect of cartel fines: 1 % to 15 % (Buccirossi and Spagnolo 2007: 95), 5 % to 20 % (Allain et al. 2015), 10 % and a rescaled markup ranging from 17 % to 27 % (Allain et al. 2011).
We assume in our simulations an interval 5 %–20 % for G.
Illegal profits are estimated as a fixed percentage of the affected market, ranging from 10 % (Werden and Simon 1987) over 20 % (Wils 2006) and 29 % (Connor and Bolotova 2006) up to 150 % (Veljanovski 2007).
Illegal profits result from cartel overcharges. Therefore, cartel overcharges – defined as the difference between the collusive price and the counterfactual “but for” price, in general the competitive price – are also used to estimate illegal profits. Connor (2004) reports a median overcharge for all types of cartels over all time periods (based on 674 observations of long-run overcharges) of 25 % (18 % for domestic cartels, 32 % for international cartels and 28 % for all successful cartels). As for overcharges outside the United States (based on 62 decisions of commissions), the median (mean) turns out to be 29 % (49 %). Based on numerous empirical studies, Combe and Monnier (2009) find it reasonable to assume a 20 % and 30 % average price increase for national and international cartels, respectively.Connor and Bolotova (2006) – surveying more than a thousand estimates of cartel overcharges throughout the centuries worldwide – estimate an average overcharge close to 22 %, with a median of 20 % (see also Bolotova 2009; Schinkel 2007). Allain et al. (2011) argue that the estimates of Connor and Bolotova suffer from an upward bias and calculate a mean value of 17.5 % (see also Katsoulacos and Ulph (2013)). Smuda (2012) calculates mean and median overcharge rates for the European market of 20.70% and 18.37% of the selling price.
Schinkel (2007) concludes: “(It) is likely to be conservative to conclude that a representative cartel manages to establish (annual) illegal gains of roughly 25 % of total annual affected commerce” (Schinkel 2007:144).
For the simulation, we assume an interval for A ranging from 10 % to 30 %.
From the beginning of cartels prosecution on the European level up to the end of 2008, the average fine amounts to 116 million euros per cartel (Combe and Monnier 2009: 3). Carree, Günster, and Schinkel (2010), Combe and Monnier (2009) and Schinkel (2007) report an upward trend in the level of fines in Europe per type of economic conduct per enforcement period. Since 2006, average fines per cartel exceed 300 million euros (Combe and Monnier 2009: 4).
Cartel fines are set in a two-step procedure according to the 2006 “Guidelines on the method of setting fines” (European Commission 2006). In the first step, a so-called basic amount is determined by “referring to the value of the sales of goods or services to which the infringement relates (European Commission 2006, Introduction, point 6). According to recital 19 of the Guidelines “(the) basic amount will be related to a proportion of the value of sales, depending on the degree of gravity of the infringement, multiplied by the number of years of infringement.” The Commission can take a proportion of up to 30 % of the value of sales (European Commission 2006, recital 21) – usually it chooses 15 %–20 %. For deterrence reasons, the Commission “will include in the basic amount a sum of between 15 % and 25 %” of the relevant value of sales (European Commission 2006, recital 25). So-called entry-fee.
In the second step, this basic amount can be adjusted upward (due to aggravating circumstances, European Commission 2006, recital 28) or downward (due to mitigating circumstances, European Commission 2006, recital 29).
Article 23 of Regulation No 1/2003 stipulates a maximum of the fine of 10 % of total turnover in the preceding business year.
We run a simulation for parameter range .
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