Collusion among many firms: The disciplinary power of targeted punishment

Journal of Economic Behavior & Organization 116 (2015) 83–93

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Journal of Economic Behavior & Organization journal homepage: www.elsevier.com/locate/jebo

Collusion among many firms: The disciplinary power of targeted punishment夽 Catherine Roux a , Christian Thöni b,∗ a b

FGN-HSG, University of St. Gallen, 9000 St. Gallen, Switzerland FDSCAP, University of Lausanne, Bâtiment Internef, UNIL-Dorigny, 1015 Lausanne, Switzerland

a r t i c l e

i n f o

a b s t r a c t

Article history: Received 5 November 2013 Received in revised form 6 March 2015 Accepted 27 March 2015 Available online 15 April 2015

We explore targeted punishment as an explanation for collusion among many firms. We run a series of Cournot oligopoly experiments with and without the possibility of targeting punishment at specific market participants. In markets with two, four, six, and eight firms, we analyze to what extent targeted punishment helps firms to restrict output. We find that targeted punishment leads to more collusion across all markets. Furthermore, beyond two firms, this collusive effect turns out to be even stronger in markets with more competitors, suggesting a reversal of the conventional wisdom that collusion is easier with fewer firms. © 2015 Elsevier B.V. All rights reserved.

JEL classification: L13 K21 C91 Keywords: Cournot oligopoly Experiments Collusion Targeted punishment

1. Introduction It is a conventional wisdom that collusion is easier with fewer firms (Chamberlin, 1933; Bain, 1951; Stigler, 1964). Both theoretical arguments and experimental studies support this assertion. In the theory of collusion in repeated games, deviations from a collusive agreement are punished with a reversion to competitive conditions which hits not only defectors, but all members of the collusive agreement (Friedman, 1971; Green and Porter, 1984; Abreu, 1988). The strength of this punishment and, thus, the firms’ incentives to collude, decrease as the number of competitors increases.1 In his seminal paper, Selten (1973, p. 141) argues that “4 are few and 6 are many” referring to five as the number of firms that separates a small group of firms from a large one. Experimental tests of the tacit collusion model have so far produced an even starker

夽 We thank the editors and two anonymous referees for helpful comments and suggestions. We are particularly grateful to Maria Bigoni, Aaron Edlin, Simon Gächter, Joseph Harrington, Nick Netzer, Nikos Nikiforakis, Hans-Theo Normann, Daniele Nosenzo, María Sáez Martí, Christian Rojas, Luís SantosPinto, Armin Schmutzler, Andrzej Skrzypacz, Adriaan Soetevent, Giancarlo Spagnolo and Roberto Weber for valuable comments and discussions. We would also like to thank participants at various conferences and seminars. Financial support from the Richard Büchner-Stiftung is gratefully acknowledged. The usual disclaimer applies. ∗ Corresponding author. Tel.: +41 21 692 28 43. E-mail addresses: [email protected] (C. Roux), [email protected] (C. Thöni). 1 In the textbook example of infinitely repeated Cournot competition (linear demand and constant marginal costs) the minimum discount rate that can ı ≡ (n + 1) /(n2 + 6n + 1). This expression is increasing in n. sustain the fully collusive outcome is  2

http://dx.doi.org/10.1016/j.jebo.2015.03.018 0167-2681/© 2015 Elsevier B.V. All rights reserved.

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C. Roux, C. Thöni / Journal of Economic Behavior & Organization 116 (2015) 83–93

finding, namely, that while collusion sometimes occurs with two firms, behavior is close to Nash play in markets with three or more firms (Huck et al., 2004).2 Yet, the reality of antitrust enforcement is different: cartels often involve many firms. Empirical evidence suggests that the median number of cartel members lies between six and ten (Posner, 1970; Hay and Kelley, 1974; Fraas and Greer, 1977), and cartels with more than a dozen members are common.3 While this type of evidence is obviously hard to find for tacit collusive agreements, a few cases indicate that these agreements exhibit a similar pattern. In 1994, for example, about 60 independent NASDAQ market makers systematically followed an implicit collusive scheme when quoting several actively traded stocks (Christie and Schultz, 1994, 1995). We suggest that real firms use richer punishment strategies than those studied in the theoretical and experimental oligopoly literature. We investigate targeted punishment, that is, punishment which is intended to hurt a particular member of the collusive scheme, as an explanation for the frequent occurrence of collusion among many firms. To this end, we run a series of Cournot oligopoly experiments with and without the possibility of targeted punishment. We design markets with two, four, six, and eight firms and analyze to what extent targeted punishment helps firms to restrict output. We have three main results. First, we find strong evidence that targeted punishment enhances collusion. In particular, we observe that in many of our experimental markets quantities converge to the perfectly collusive output. Second, when we systematically vary the number of firms, we find that the collusive effect of targeted punishment tends to be stronger in markets with more firms. This finding suggests a reversal of the conventional wisdom for markets with four firms and more and is novel for oligopoly experiments. Third, our data confirm an interesting finding in the literature on the organizational structure and workings of cartels, namely, that more severe deviations trigger harsher punishment (Genesove and Mullin, 2001). Firms fine-tune their retaliation to hit harder those who produce more damage to the colluding firms. Targeted punishment is widely used in practice. A close examination of about 20 recent cartel cases in Europe leads Harrington (2006, p. 40) to the conclusion that “typically, though not universally, the threatened aggression would be targeted at the markets and customers of the deviator.” In the industrial and medical gases cartel, for example, suppliers maintained lists for each competitor which indicated the price concessions they had to accept because of competitive offers made by that particular competitor. Together with information on that competitor’s potentially interesting customers, a supplier could set up “hit lists” for a targeted retaliation campaign referred to as the “balance of terror”.4 Another example comes from the lysine cartel: when the Korean company Sewon announced an increase of sales above its allocated quota, the cartel member Ajinomoto responded with a threat to file an anti-dumping complaint in Europe.5 Targeted punishment mechanisms are also used in tacit collusive agreements. One possible form of such punishment are the social sanctions to which individual representatives of defecting firms are commonly exposed. In the NASDAQ conspiracy, for example, although it consisted of an implicit agreement, a maverick dealer that narrowed the spread when quoting his stocks was easily identified. The screen-based system displayed the quotes of every market maker and thus made the market essentially transparent (Christie and Schultz, 1995). Targeted punishment could then happen explicitly by overt harassment of the maverick dealers: “You’re embarrassing and pathetic. . . . You’re breaking the spreads for everybody.” (Paltrow, 1994, p. 1).6 While typical examples of targeted punishment in oligopolies involve targeted price cutting and social sanctions, this punishment can take many different forms: exclusive-dealing contracts with the suppliers of the essential industry input (Krattenmaker and Salop, 1986), comparative advertising strategies against the defector (Ayres, 1987), or simply the expulsion of the agreement (Dick, 1996). The remainder of this paper is organized as follows. Section 2 describes the experimental design. Section 3 explains the hypotheses. Section 4 discusses our results, and Section 5 concludes.

2. Experimental design and procedures We investigate the effect of targeted punishment in markets with two to eight firms. Subjects either play a standard Cournot game or a game with targeted punishment possibilities (Punishment). We focus on tacit collusion and do not allow for communication among the participants. Cournot consists of 20 periods of our basic game in which n ∈ {2, 4, 6, 8} symmetric firms face linear demand and produce at constant marginal cost. The firms simultaneously and independently choose a 74 with 0.1 as the quantity for the production of a homogeneous good. Their action sets are numbers between 0 and  n smallest increment.7 The price is determined by the market demand P = max {74 − Q, 0} where Q = q is the total i=1 i

2 See Huck et al. (2001) for a comparison with collusion in experimental Stackelberg oligopolies and Engel (2007), Haan et al. (2009), or Potters and Suetens (2013) for reviews of the experimental literature on oligopoly experiments and collusion. 3 See for example the cartel in prestressing steel with 17 and in copper fittings with 30 companies (EC IP/11/403 and EC IP/06/1222). 4 OJ L 84/1, 1.4.2003, 83, p. 12. 5 OJ L 152/24, 7.6.2001, 88, p. 34 and Harrington (2006). 6 Christie and Schultz (1995) also discuss a number of possible sanctions that can be effectively used to punish a designated market maker but do not require any form of overt communication. 7 We introduce an upper bound of 74 to prevent firms from making large losses which occur when they choose excessively high quantities. Note that the upper bound still allows each subject to drive the market price down to zero on his own.

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quantity produced in the market. The marginal costs of production are equal to 2. In addition, each firm receives a per-period endowment of 20 units. Firm i’s profit in a given period is i1 = max{74 − Q, 0} · qi − 2 · qi + 20.

(1)

At the end of each period, the firms are informed about all individual quantities and profits realized in the market. In Punishment, the game consists of two stages. The first stage is identical to the Cournot game. After having learned the quantities of the other firms, subjects proceed to the second stage, where they can punish the other firms in the market. Firms assign punishment points pij that reduce of the punished firm j by five units at a cost of one unit to the  the payoff 8 punishing firm i, with pij ∈ {0, 1, . . ., 20} and j pij  20. The lump-sum payment of 20 units allows the firms to cover the costs of punishment. Units not used for punishment contribute to the firm’s profits.9 Firm i’s profit in a given period is i = i1 − 5 ·

 j= / i

pji −



pij .

(2)

j= / i

At the end of the second stage, the firms learn the total number of punishment points they received from other market participants and their profit of the period. In both conditions, the game is played as a finitely repeated game with 20 periods in a partner matching protocol. We apply a within-subjects design. In a typical experimental session, subjects play 20 periods of Cournot followed by 20 periods of Punishment. Subjects only read the instructions for part two after the first part has ended. To control for order effects, we ran two sessions with two and four-firm oligopolies in the reversed order. All game parameters and the number of periods are commonly known. Assuming subgame perfection and common knowledge of rationality, the punishment option should not affect the outcome of stage one. Both games Cournot and Punishment have a Nash equilibrium where all firms chose qi = qN = 72/(n + 1). Firms maximize joint profits by choosing qi = qC = 36/n. The sessions were run in the lab at the University of St. Gallen between February and October 2012 and were programmed in z-Tree (Fischbacher, 2007). Recruitment was carried out with ORSEE (Greiner, 2004). Subjects were randomly allocated to the computer terminals in the lab so that they could not infer with whom they would interact. We provided written instructions which informed the subjects of all the market features, and we read out loud the most important points.10 Similar to other studies on experimental Cournot games, we used an economic framing and told the subjects that they were representing a manager of a firm in a market with n − 1 other firms, and that their job was to make output decisions (see, for example, Huck et al. (2004)). Before the start of each treatment, the subjects had to answer a control question.11 When answering the control question and when choosing the quantity during the game, the subjects had access to a profit calculator, allowing them to calculate the payoff of hypothetical combinations of their quantity and the mean quantity produced by their competitors. For the profits during the experiment, we used an experimental currency unit called Guilders, and 1000 Guilders were worth 1.10 CHF for the duopolies. We adapted the exchange rate for the four, six and eight-firm markets so that the Nash earnings would be equalized across markets. The payments consisted of a 10 CHF show-up fee plus the sum of the profits over the course of the experiment. Potential losses were deducted from the show-up fee. None of our subjects went home empty handed. The sessions lasted for about 105 minutes, and the mean earnings were about 37 CHF (ranging from 17 CHF to 43 CHF, 37 CHF ∼39 USD). The 152 subjects were undergraduate students in economics, business, international studies, and law, and had not participated in oligopoly experiments before. 3. Hypotheses We begin with the conventional wisdom that establishing and maintaining collusion becomes more difficult with more firms. We expect to replicate the results of Huck et al. (2004) in our Cournot condition and thus, we put forward the following hypothesis.

8 The design of the punishment stage is inspired by the literature on public goods games with punishment (Chaudhuri, 2011), but we apply a ‘fine-to-fee’ ratio of punishment of five-to-one rather than the frequently used three-to-one. The reason for this adaption is that the relative profits which firms can attain when deviating from cooperation in our Cournot markets are much higher than in the standard public goods case. To make targeted punishment similarly effective, we increase that factor from three to five. 9 This lump-sum payment is identical for all n. Maximum punishment targeted at a single firm is thus strongly increasing in n, from 100 in n = 2 to 700 in n = 8. However, at the same time, the payoff gains from unilateral deviation increase (from 81 to 248), and the number of potential targets (non-collusive firms) increases in n. In addition, coordinating punishment among the collusive firms is likely to be more difficult with more firms. Consequently, it is not clear whether each firm’s budget constraint is more or less restrictive as n increases. An alternative would have been to give no specific budget for total punishment as e.g. Carpenter (2007), and just subtract the expenses from the subject’s profit. In any case it is important to note that, for all n, our punishment technology is linear and has an identical fine-to-fee ratio (Casari, 2005; Nikiforakis and Normann, 2007). To maintain comparability between Punishment and Cournot, the endowment of 20 was also paid in the latter. 10 An English translation of the experimental instructions is available in the online supplement. 11 We presented the subjects with a randomly generated combination of the own quantity and the mean quantity of the other players, and their task was to calculate their payoff. In a methodological note, we check whether the presented situation influences the quantities in the first period (Roux and Thöni, forthcoming). We find no evidence for such an effect.

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Hypothesis 1.

C. Roux, C. Thöni / Journal of Economic Behavior & Organization 116 (2015) 83–93

Without targeted punishment, the total quantities increase with the number of firms.

Next, we consider the impact of targeted punishment on collusion. We designed the punishment stage similar to the design used in the literature on public goods games with punishment. The upshot of this literature is that punishment stabilizes cooperation very effectively (Fehr and Gächter, 2000; Herrmann et al., 2008).12 Whether this punishment mechanism has comparable effects in Cournot games is however not immediate.13 Nevertheless, we hypothesize that targeted punishment helps to establish and sustain collusive agreements. Hypothesis 2.

For all numbers of firms, quantities are lower when targeted punishment is available.

Finally, we explore the question whether the availability of targeted punishment can undermine the conventional wisdom. Intuitively, there are several forces that work in opposite directions. On the one hand, the potential harm caused by targeted punishment increases with the number of firms that can target punishment at a defector. On the other hand, the larger the group that can punish, the more likely it is that each individual firm may actually want to free-ride on others’ punishments.14 Furthermore, with more firms the number of potential defectors increases. Interestingly, in the large literature on public goods games with punishment, there is hardly any evidence on the effects of a systematic variation of the group size. A notable exception is Carpenter (2007), who observes groups of five and ten subjects and finds that the larger groups tend to contribute more to the public good than the smaller groups. In particular, the findings indicate that the strength of individual punishment imposed on a deviator is to some degree invariant to group size, leading to stronger overall punishment in larger groups. If this also applies to Cournot games we should see that larger groups find it easier to collude. Hypothesis 3.

With targeted punishment, the total quantities decrease as the number of firms increases.

4. Results In the following, we discuss our experimental results in the order of the hypotheses. Beforehand, a few general remarks about the data analysis and the statistical inference are warranted. For the two and four-firm oligopolies we observe both treatment orders. As none of the statistical tests indicates that order effects are important, we pool the data of both orders.15 In the figures we sometimes report the median instead of the mean quantities because the latter are affected by asymmetric outliers. Medians are calculated based on the individual outcomes in the respective category. For all statistical tests, we either use independent group means as unit of observations or estimate standard errors clustered on group level. Group means of quantity and punishment decisions are reported in Appendix A (Table A.1). 4.1. The number of firms and the impact of targeted punishment We first examine whether the conventional wisdom that collusion is easier with fewer firms holds in the Cournot condition. Fig. 1 shows the median of the total quantities produced across all markets in both conditions. The lower horizontal line shows the collusive situation which is the total quantity produced in monopoly. The upper horizontal lines show the total quantity predicted in the Nash equilibrium. From the left panel, we can see that the total quantities increase with group size from two to six firms in the Cournot condition. The increase in total quantity with increasing numbers of firms is highly significant (p < .001, Jonckheere–Terpstra test16 ). While play in the duopolies lies in between Nash and collusion, the oligopolies with four, six, and eight firms tend to produce above the Nash prediction.17 These findings support Hypothesis 1 and are in line with the results reported in Huck et al. (2004).

12 In this literature, the distinction between targeted and non-targeted punishment is usually not made, such that any mentioning of punishment refers to targeted punishment. 13 If we define playing the Nash equilibrium as free riding and playing the collusive quantity as cooperation, then the two games have a very similar incentive structure. What we know from the literature shows that the transfer between games is, however, not so straightforward. Repeated public goods games in groups of four subjects typically result in mean contributions at around 50 percent of the endowment early in the game, that is, produce quite cooperative results. With repeated interaction contributions drop, but means close to zero are typically not observed until the very end of the game (see, for example, Herrmann et al. (2008)). On the other hand, in repeated Cournot games with four firms there is hardly any indication of collusive behavior, not even in the initial phase (see, for example, Huck et al. (2004), or our results below). The reason may be that the Cournot and the public goods game differ in two important dimensions. Unlike the standard public goods game the Cournot game has an interior solution, and non-trivial reaction functions. 14 This effect is equivalent to the bystander effect in social psychology first identified by Darley and Latane (1968). The results from public goods games with punishment suggest that this second-order free-rider problem does not hamper the effectiveness of the punishment mechanism too much (Fehr and Gächter, 2000). 15 Tests for differences in quantities between first and second order give p = .451 (p = .445) for n = 2 (4) in Cournot and p = .681 (p = .628) in Punishment (exact Wilcoxon rank-sum tests). We observe 9(7) groups in the main order, and 7(6) in the reversed order for n = 2 (n = 4)). 16 Similar to the Kruskal–Wallis test, the Jonckheere–Terpstra test is a non-parametric test for whether samples (in our case group means for the different numbers of firms) originate from the same distribution. Unlike the Kruskal–Wallis test, this test has an ordered alternative hypothesis. As a parametric alternative, we ran a simple linear regression explaining the total quantities by n. The results are similar. 17 The differences to Nash are insignificant with p > .1 except for six-firm oligopolies, which produce weakly significantly higher total quantities (p = .063, exact Wilcoxon signed-rank test).

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Punishment

60 50 40 30

Total quantity (median)

70

Cournot

87

2

4

6

8

2

4

6

8

Number of firms (n) Fig. 1. Median of total quantities in Cournot and Punishment for all numbers of firms. Horizontal lines indicate the theoretical benchmarks: collusion (lower) and Nash equilibrium (higher). Table 1 Quantities: theory, experiment, and treatment effect. n

Firms

Markets

Quantities

p-value

Theory

2 4 6 8

32 52 36 32

16 13 6 4

Experiment

Nash

Collusion

Cournot

Punishment

24 14.4 10.3 8

18 9 6 4.5

22.69 14.96 11.45 8.42

20.07 12.53 7.61 5.50

.005 .001 .016 .063

Notes: Number of observations and theoretical and observed firms’ mean quantities. The last column shows exact p-values from one-sided Wilcoxon signed-rank tests for differences in the distribution of firms’ quantities between Cournot and Punishment.

Result 1. Without targeted punishment, the total quantities increase with the number of firms and are close to or above the Nash quantities for n > 2. Turning to the Punishment condition, we can see from the right panel of Fig. 1 that total quantities substantially decrease for all group sizes. The duopolies produce quantities close to the collusive benchmark, while the oligopolies with four, six, and eight firms produce quantities in between collusion and Nash. Table 1 shows the mean quantities in Cournot and Punishment. For all markets, treatment differences are significant.18 We can thus reject the null hypothesis that targeted punishment has no effect on the firms’ ability to collude. If we compare the quantities to the theoretical benchmarks we observe that firms produce significantly less than the Nash quantity in all markets.19 Fig. 2 shows the dynamics of play. The quantities are measured on the left vertical axis. Bold lines show the median quantity over the 20 periods of Cournot and Punishment for each number of firms. Thin lines show mean quantities, which are almost always higher than the median quantities. The horizontal thin lines show the theoretical benchmarks. The bars show the mean number of individual punishment points used to reduce the other firms’ payoffs (right vertical axis). Fig. 2 displays no tendency towards collusion during the 20 periods of Cournot, while targeted punishment often leads to output close to the collusive benchmark. In all but the four-firm oligopolies, the collusive quantity is the median choice in the last third of Punishment.20 Thus, it is the introduction of targeted punishment and not experience that allows firms to collude. Overall, these results support Hypothesis 2. Result 2.

The availability of targeted punishment substantially reduces quantities for all numbers of firms.

The bars in Fig. 2 indicate that the punishment option is effectively used throughout all periods, that is, establishing collusion comes at a cost. We may thus be concerned that the use of targeted punishment lowers firms’ profits. This is,

18 We report the one-sided p-values because we have a directed hypothesis. The fact that the p-value for the eight-firm oligopolies is only weakly significant is mainly due to the use of a conservative test. The corresponding t-test gives p = .002. 19 The quantities lie above the collusive benchmark. The difference is significant at 5% for all group sizes except eight, even though the median quantity for n = 2 is very close to the collusive output (Wilcoxon signed-rank tests). The reason is that the deviations are almost exclusively towards higher quantities, that is, deviating subjects very rarely undercut the collusive quantity. 20 For n = 2, the median quantity is (with one exception) 18.5. Most duopolies coordinated on this quantity and not on the qC we derived above (18). Due to the fact that we round each payoff to an integer, both situations lead to identical payoffs.

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n=4

6

20

20 10

10

8

0

20 20 1

1

20 1

20

n=8 12

n=6 Punishment

Cournot

Punishment

20

20

6

8

8

10

12

10

14

Cournot

Punishment

0

22 20 18 16 1

Cournot

10

4

1

20 1

20

0

0

4

10

6

Quantity (bold: median, thin: mean)

24

Punishment

10 12 14 16 18 20

26

n=2 Cournot

Punishment (bars)

88

1

20 1

20

Period Fig. 2. Firms’ quantities across markets and periods. Bold lines indicate median quantities, thin lines indicate mean quantities. For the sessions with reversed order, we reordered the observations such that Cournot is displayed first. The two horizontal lines indicate the theoretical benchmarks: collusion (lower) and Nash equilibrium (higher). Bars indicate the mean number of punishment points assigned to other firms in a given period of Punishment.

however, not the case: for all markets mean profits are higher with the punishment option. The six- and eight-firm oligopolies almost double their payoffs in Punishment (increases of 95% and 94%). In the duopolies and the four-firm oligopolies, the increase in profits of 7% and 16%, respectively, is relatively moderate. In Hypothesis 3, we conjecture the reversal of the conventional wisdom in Punishment. Fig. 1 shows that our evidence is mixed: increasing the number of firms from two to four significantly increases the total quantity (p = .003, exact Wilcoxon rank-sum test). If we consider only the markets with four and more firms, we observe that total quantities decrease when the number of firms increases (p = .037, Jonckheere–Terpstra test, one-sided). This is consistent with the results of Carpenter (2007), who observes higher contributions in groups of ten than in groups of five in public goods games with punishment. Thus, apart from the duopoly case, we receive support for Hypothesis 3. Result 3.

Total quantities decrease with the number of firms for n > 2 when targeted punishment is available.

One may argue that the size of the treatment effect, that is, the difference between the total quantities produced in Cournot and Punishment, is a more accurate measure for the anticompetitive effect of the punishment option than the total quantity per se. When we compare the difference between the bars in Fig. 1 across firm numbers, we observe a very clear positive effect (p < .001, Jonckheere–Terpstra test). 4.2. The disciplinary power of targeted punishment Why does the collusive effect of targeted punishment increase with the number of firms? The key to this result lies in how the number of firms affects the disciplinary power of the punishment option. The majority of the market participants use targeted punishment. Among the 152 participants only 19 never punish during the 20 periods, and many of them are in groups which collude almost perfectly. On average, firms in n = {2, 4, 6, 8} spend {1.31, 9.45, 8.73, 5.45} of their endowment of 20 units on punishment. Interpreting these numbers in isolation is difficult because punishment is presumably affected by the quantities the firms choose in the first stage. This is also suggested by the bars in Fig. 2, which show lower amounts of punishment in periods where quantities are close to the collusive outcome. To better understand what determines targeted punishment, we ran OLS regressions with robust standard errors clustered on independent groups.21 The dependent variable is the sum of punishment points received by firm i from the other n − 1 market participants. The independent variables are firm i’s quantity and a number of controls. We rescaled firm i’s quantity

21

Tobit estimates yield similar results.

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Table 2 Determinants of getting punished: regression results. Dependent variable: Sum of received punishment

qri × (n = 2) qri × (n = 4) qri × (n = 6) qri × (n = 8) q¯ r−i n = 2 (D) n = 4 (D) n = 6 (D) n = 8 (D) Period Final period (D) Order C → P (D) F-test Prob >F R2 N

(1)

(2)

2.742** (1.354) 19.938*** (5.240) 66.135*** (8.457) 90.112*** (9.217) −4.214*** (1.929) 0.730 (1.024) 4.328** (1.738) 0.510 (1.730) −1.541 (1.608) 0.033 (0.062) −0.177 (0.914) 1.226 (1.217)

9.258*** (3.322) 50.742*** (5.197) 95.332*** (9.128) 112.533*** (9.024)

87.9 0.000 0.595 3040

53.8 0.000 0.756 1330

−1.410 (1.168) 2.718 (2.041) 2.917 (2.120) −0.708 (1.477) 0.032 (0.088) 1.745 (1.150) 1.854 (1.187)

Notes: OLS estimates. Dependent variable is the sum of punishment points received by firm i from all other firms in the group. Independent variables are the rescaled quantity qri = (qi − qC )/(qD − qC ), where qri = 0 if firm i produces the collusive output and qri = 1 if firm i produces the best-response quantity to the collusive quantities of the other firms, and dummies for the number of competitors and interactions. Further controls are the average rescaled quantity of the other firms in the group (q¯ r−i ), Period ∈{1, 2, . . ., 20}, Final period is a dummy for the last period. Order C → P is a dummy for the treatment order. Model (1) reports estimates using the whole sample, in Model (2) we restrict the sample to q¯ −i − qC  1, i.e., we consider only cases in which the n − 1 other firms choose collusive quantities. Robust standard errors, clustered on group, in parentheses. *p < 0.1, ** p < 0.05, ** * p < 0.01.

to qri = (qi − qC )/(qD − qC ) where qC denotes the collusive quantity and qD = 18(n + 1)/n denotes the ‘optimal deviation,’ that is, the best-response quantity for the situation in which the n − 1 other firms choose the collusive quantity. Thus, qri is a linear transformation of qi such that, independently of the number of firms, qri = 0 if firm i chooses the collusive output and qri = 1 if firm i chooses the optimal deviation. This rescaling allows a straightforward comparison of the coefficients between markets with different numbers of firms. We estimate the coefficient for qri separately for each number of firms. Model (1) in Table 2 reveals that there are huge differences in received punishment. Comparing firms which produce the collusive quantity (qri = 0) to those which optimally deviate (qri = 1) shows that the increase in punishment ranges from merely 2.7 units for duopolies to 90 units for eight-firm oligopolies. Each received punishment point reduces the punished firm’s payoff by five units, and thus, the coefficients multiplied by five give the estimated income reduction. Model (1) includes the mean quantity of the other firms in the market, rescaled by the same procedure as firm i’s quantity, as a control. The coefficient estimate for q¯ r−i is negative, meaning that high quantities of the other firms reduce the amount of punishment. Hence, punishment becomes stronger when the other firms are closer to perfect collusion.22 We include four dummy variables for the different numbers of firms (and estimate without constant). Most of these dummies are insignificant.23 We include the period number and a dummy for the final period to capture end-game effects in punishment, and we add a dummy for the order in which the treatments were conducted. None of these variables seem to have a systematic impact on received punishment.

22 We also ran a model estimating the effect of q¯ r−i separately for each number of firms. The effect is significant in all cases except for n = 2. The coefficients for the slopes in qri are very similar to those shown in Model (1). 23 The significant coefficient for n = 4 is not an indication for punishment independent of the quantity but is rather due to the fact that the linear model does not describe punishment very well in case of n = 4. If we add a quadratic term for qri the dummy becomes insignificant, with a significantly positive (negative) linear (quadratic) term.

90

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In Model (2), we restrict our sample to the cases with |q¯ −i − qC |  1, that is, situations where the other firms’ quantities are, on average, close to the collusive quantity.24 This procedure leaves us with 1330 observations. Model (2) comes closest to estimating the punishment targeted at a firm which unilaterally deviates from a collusive agreement. The coefficients of the slopes are larger than in Model (1), reinforcing the argument that punishment is harshest when the rest of the group remains in a collusive agreement. When we multiply the coefficients by five, we get an estimate for the income reduction an ‘optimal’ deviator faces, namely {46.3, 254, 477, 563} for n = {2, 4, 6, 8}. We have to set these numbers in relation to the maximum profits that can be earned by optimally deviating from a collusive agreement, which are {81, 182, 225, 248}. While for duopolists deviating from collusion might pay in the particular period it does not for firms in oligopolies with more than two competitors. Punishment is not only strong on average, it is also quite certain to occur. If we consider the cases where n − 1 firms play on average qC ± 1 (as in Model (2)) and calculate the frequency that a deviating firm i with qi > qC + 1 will be punished, we see that a duopolist receives punishment in 59% of the cases. In all markets with n > 2, there is not a single instance, out of 80 cases, in which the deviator gets away unpunished. When we divide the number of punishment points assigned to the defecting firm by the number of potential punishers we observe almost no reduction with increased group size {9.26, 16.9, 19.1, 16.1}.25 For n > 2, punishment is usually coming from more than one other firm. Conditional on being punished, the mean number of punishers increases from 1.6 to 2.4 from n = 4 to n = 8. For a firm with a quantity strictly larger than all other quantities in the market, the mean number of punishers is {2.2, 3.8, 5.0} in n = {4, 6, 8}. Taken together, the results above suggest a reason for the reversal of the conventional wisdom in our Punishment condition: subjects do not adjust their punishment per deviation to the different group sizes. Consequently, a deviator faces much harsher punishment in markets with more firms. This is remarkable because, in markets with more than two firms, the punishment of deviators is a pure public good. When it comes to enforcing collusive agreements it seems that larger groups are not plagued by the bystander effect. There is, however, one caveat to that: the gain from targeted punishment in terms of collusive ability may well be non-monotonic in the number of firms. Such a pattern has been observed by Fonseca and Normann (2012) with respect to the gain from communication in collusive agreements with a various number of firms. As the maximum number of oligopolists in our experiment is eight, it remains an open question how the effect of targeted punishment evolves for even larger groups. 4.3. The role of damage severity Models (1) and (2) in Table 2 indicate that the quantity choice is an important predictor for the punishment decision. In the next step, we investigate the punishment from a slightly different angle and show that the received income reduction is gradually increasing in the damage a deviating firm inflicts on the other firms in its market. We denote by −i (qi , qj , . . .) the ˆ −i (q¯ −i , qj , . . .) that would have been sum of the profits of the n − 1 other firms, and relate this to the counterfactual profit  realized, had firm i chosen a quantity equal to the mean quantity produced by the other firms in its market. Whenever firm i offers more than the other firms’ mean quantities, the produced damage is positive, while a firm with a smaller quantity produces a benefit to others (a negative damage). With very few exceptions, this measure for damage is in the range of ±500. Fig. 3 shows the results. Punishment targeted at firms with low quantities is virtually zero.26 Firms which inflict damage on other firms face a punishment which is gradually increasing in the damage, at least for the markets with n > 2. For instance, in the markets with n = 8, the profit of a firm causing damage between 50 and 150 is on average reduced by slightly more than 100 units, whereas for a firm causing damage between 150 and 250, the reduction amounts to about 200 units in the punishment stage. This result confirms Genesove and Mullin’s (2001) finding from the study of the Sugar Institute cartel that punishment “fits the crime.” Result 4. For n > 2, the income reduction imposed on the deviating firm is gradually increasing in the damage this firm inflicts on the other firms in the market. 5. Discussion and conclusion A conventional wisdom is that collusion is easier with fewer firms. While theories on collusion as well as oligopoly experiments support this assertion, there is abundant evidence on convicted cartels suggesting that firms manage to cooperate also in markets with a large number of competitors. Moreover, firms in these markets target punishment at specific cartel

24 As we only rarely observe quantities below qC , this means that the other firms’ quantities are relatively similar. We define the interval of qC ± 1 as ‘close’. We get similar results if we restrict the others’ average to qC ± .5. For larger intervals, the estimated coefficients converge to Model (1). 25 The increase between n = 2 and n = 4 is significant (p = .040, F-test). This increase might be due to the fact that in duopolies, all punishment is targeted, that is, both an increase in quantity and the assignment of punishment points harm the deviating firm exclusively. All other differences are insignificant (p > .17). 26 In the literature on public goods games such punishment targeted at cooperative subjects is referred to as antisocial punishment (Herrmann et al., 2008), or perverse punishment (Bochet et al., 2006). The former study documents widely different levels of antisocial punishment across 16 subject pools around the globe and shows that its occurrence substantially reduces cooperation. It is likely that higher levels of punishment towards firms with low quantities would have a similar effect in Cournot games and lead to more competitive outcomes.

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n=4 n=8

0

50 ,3 [2

50

>3 5

)

) ,2 50 [1

[5

0,

15

50

0)

) 50 0,

0) ,-5 50

[-5

) 50 [-1

,-1 50 [-2

[-3

50

,-2

<3

50

50

)

0

100

Income reduction 200 300

n=2 n=6

91

Damage Fig. 3. Income reduction due to received punishment in relation to the ‘damage’ inflicted on other firms by deviating from the others’ mean quantity.

members in order to enforce compliance with the rules of collusion. When cheating occurs, it does not immediately lead to a price war but rather triggers punishment that fits the crime. The same seems to hold true for tacit collusive agreements. In a series of Cournot oligopoly experiments with various numbers of market participants, we studied whether targeted punishment explains the occurrence and stability of collusion among many firms.27 Without targeted punishment, our results confirm earlier findings in the literature: some collusion occurs in duopolies but behavior is close to the Nash benchmark or even more aggressive in groups of four and more. But when we make targeted punishment available collusion occurs for all group sizes. Moreover, beyond two firms, the collusive effect of targeted punishment is even stronger in markets with more firms, suggesting a reversal of the conventional wisdom. Our analysis of the punishment behavior indicates that the higher the quantity a defecting firm produces, the stronger the punishment imposed by other market participants. What might drive the strong impact of targeted punishment on collusion? Our analysis shows that, unlike what is predicted using the standard assumptions, targeted punishment is a highly credible threat even in the final round of the game. The literature on non-standard preferences has mainly focused on two explanations for this phenomenon: (i) players have preferences over the distributions of the final payoffs among all players, for example, inequality aversion, and (ii) players not only consider final outcomes but also the intentions of other players, for example, reciprocity.28 The first explanation would clearly imply that in one-deviator situations (as investigated in Model (2) of Table 2), per capita punishment decreases as group size increases. Firms would simply want the deviator’s income to be lowered, but prefer others to do the dirty work.29 If reciprocity is the motive behind targeted punishment, things might look different. A revengeful firm might feel the urge to retaliate, independently of whether others do so or not. In the light of our experimental results, we find the reciprocity explanation more compelling. If reciprocity is the driver behind targeted punishment, it might be interesting for future research to explore situations in which there is ambiguity about the true intention behind an observed market outcome. There might be a multitude of reasons for firms to deviate from the collusive agreement, or the information about market quantities might be distorted.30 Another extension would be allowing communication. In real-world cartels, members usually meet and talk to coordinate actions. While communication is likely to help coordination in the quantity choice (see Fonseca and Normann (2012) for Betrand games), its effect on the disciplinary power of targeted punishment is less clear. On the one hand, deviating from an agreement in which the collusive rules have been explicitly defined may be seen as a particularly nasty action and thus spur even stronger punishment than the deviation from collusive situations in our experiment. On the other hand, communication may enable renegotiation which may weaken punishment possibilities. Our results shed an interesting light on the discussion of coordinated effects in merger decisions. The European Commission’s merger decisions published from 1990 to 2004 indicate that the potential for coordinated effects arise only if the post-merger market would include two remaining firms with fairly identical market shares (Davies et al., 2011). While this perspective, adopted by the European Commission, is in line with the existing theoretical and experimental literature, our findings suggest that it may be too narrow. Targeted punishment strategies enable firms to collude in markets with many

27 There may be many other determinants of cartel success such as the organizational structure, trade associations, barriers to market entry, monitoring schemes etc. (Levenstein and Suslow, 2006). 28 See Sobel (2005) for an overview and I˙ ris¸ and Santos-Pinto (2013) for an application to oligopolies. 29 For a detailed analysis of punishment motivated by distributional preferences, see Thöni (2013). 30 Research from public goods games suggests that imperfect information reduces the efficacy of the targeted punishment option (Grechenig et al., 2010; Ambrus and Greiner, 2012).

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firms and thus, coordinated effects may be an issue even in less concentrated post-merger markets. Our results may also be important in the antitrust evaluation of information exchanges as circumstantial evidence for collusive behavior when a hard-core agreement is absent.31 European case law suggests that whether the information exchanges are considered as unlawful is directly linked to the degree of market concentration as, in less concentrated markets, collusion is believed to be unlikely to arise. Our results suggest that lower concentration does not necessarily go hand in hand with less collusion and thus, information exchanges may still be problematic in markets with many firms. Appendix A. Data Table A.1 Summary statistics on group level. Order C → P

n

Quantity in Cournot Mean

SD

Quantity in Punishment

Punishment

Mean

SD

Mean

SD

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0

19.22 18.15 26.88 27.45 22.45 20.48 24.65 24.40 21.96 35.35 20.13 18.23 18.00 23.00 24.71 18.00

1.45 3.08 5.95 1.49 4.04 2.95 4.80 5.92 6.45 5.33 2.78 1.42 0.00 3.04 4.15 0.00

18.67 18.50 19.23 25.17 18.75 18.05 18.60 19.28 22.81 30.40 18.84 18.00 17.85 21.84 23.00 22.23

1.03 0.00 2.10 1.13 1.72 0.32 2.07 1.98 6.08 9.41 3.10 0.00 0.66 4.12 6.88 4.81

1.77 0.00 1.85 0.20 0.47 0.00 2.22 0.50 0.00 1.70 0.75 0.00 0.00 2.25 8.20 1.17

4.68 0.00 4.98 0.85 2.24 0.00 6.05 3.16 0.00 5.31 2.67 0.00 0.00 4.10 9.04 3.86

4 4 4 4 4 4 4 4 4 4 4 4 4

1 1 1 1 1 1 1 0 0 0 0 0 0

15.86 13.65 16.01 13.54 16.17 16.26 14.87 12.43 15.52 12.76 17.08 15.81 14.56

3.13 3.29 9.75 2.60 3.21 7.10 4.42 2.78 3.31 7.09 3.54 3.32 2.67

11.87 9.20 11.99 13.04 10.85 13.73 14.68 10.84 13.10 11.75 15.07 13.63 13.22

3.81 1.25 5.01 1.37 2.61 3.30 7.37 2.63 2.57 8.20 6.34 4.09 2.70

14.90 2.15 13.64 7.10 13.79 12.80 8.35 6.81 8.07 8.35 9.82 8.01 9.00

7.47 6.09 8.98 9.06 8.49 9.33 9.15 8.42 9.21 9.51 8.24 9.01 8.00

6 6 6 6 6 6

1 1 1 1 1 1

11.53 10.94 12.20 10.06 11.39 12.58

6.14 1.42 5.47 2.78 4.74 11.08

7.51 7.37 8.07 6.38 8.80 7.53

2.08 2.06 2.82 1.76 1.00 3.16

14.64 10.66 8.32 4.34 5.93 8.48

6.93 8.52 8.91 7.71 7.75 8.78

8 8 8 8

1 1 1 1

7.92 8.21 8.80 8.76

2.24 4.45 6.13 4.59

4.98 4.87 6.90 5.24

0.70 2.04 2.17 2.39

3.69 3.39 7.92 6.81

5.53 6.08 9.00 8.23

Appendix B. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/ j.jebo.2015.03.018. References Abreu, D., 1988. On the theory of infinitely repeated games with discounting. Econometrica 56, 383–396. Ambrus, A., Greiner, B., 2012. Imperfect public monitoring with costly punishment: an experimental study. Am. Econ. Rev. 102, 3317–3332.

31

See, for example, European Commission UK Agricultural Tractor Registration Exchange, OJ L 68, 13.3.1992, pp. 19–33.

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