Communication, Renegotiation and the Scope for Collusion

1. Communication, Renegotiation and the Scope for Collusion David Cooper Florida State University Kai-Uwe Kühn University of Michigan Prepared for Seminar at University of East Anglia, December 13, 2007.

2. The Theory of CollusionSuccess . . . • Theory has been very successful in describing the form a collusive equilibrium should take. • Abreu (1988) • Abreu, Pearce, and Stacchetti (1990) • The theory has been widely applied to anti-trust policy. • Motta 2004 • Compte, Jenny, and Rey 2002 • Kühn 2004 • Kühn forthcoming

3. The Standard Collusion Model The Incentive Condition: Loss from switching to a worse equilibrium in the future Benefit from undercutting by one unit

4. The Theory of Collusion. . . and Failure • The theory does not provide a satisfying answer for how players coordinate on a particular collusive equilibrium. • Bargaining over equilibrium value set (Harrington 1991; Kühn and Rimler 2006) • Renegotiation (Bernheim and Ray 1989; Farrell and Maskin 1989; Van Damme 1989; Pearce 1987; Abreu, Pearce, and Stacchetti 1993) • Cheap talk need not yield efficiency (Farrell 1993; Farrell and Rabin 1996; and Rabin 1994) • Empirical literature on factors making collusion more likely cannot distinguish between process leading to collusion and conditions that affect the incentive conditions of standard theory.

5. Unresolved Problems in Collusion Theory • Explicit vs. Tacit Collusion • Explicit Collusion: • How much does communication matter? • Does collusion require specifying contingent strategies? • Are feelings of spite or other “fairness” a sufficient enforcement mechanism for collusion? • Renegotiation: • Does it severely limit collusion as theory suggests?

6. Communication to coordinate • Simple coordination games • In Collusion Models: • Coordination on contingent strategies necessary • Much greater complexity: Not coordination on simple actions, but on contingent rules necessary for the theory to be relevant

7. Experiments on Collusion • There exists an extensive experimental literature on collusion. • Collusion more likely when consistent with equilibrium (Roth and Murnighan, 1978; Murnighan and Roth, 1983; Palfrey and Rosenthal, 1994; Aoyagi and Fréchette, 2003; and Dal Bó, 2005). • Finite vs. Indefinite Repetition (Dal Bó, 2005) • Matching protocols (Duffy and Ochs, 2003) • Risk Dominance (Dal Bó and Frechette, 2007) • It is well established that allowing communication can improve collusion (Dawes, MacTavish, and Shaklee, 1977; Davis and Holt, 1990).

8. Communication and Collusion • This paper focuses on the role of communication in fostering collusion. • Our goal is not to show that allowing communication can increase collusive behavior – this is already known to be true. • Our goal is establish what feature of communication are critical for establishing collusion. • Contingent strategies • Renegotiation • Content analysis • Is improvement transient or persistent?

9. Two Stage Bertrand Game • The underlying game being played by subjects is an infinitely repeated Bertrand duopoly game. • In the spirit of Abreu, Pearce, and Stacchetti (1990), we collapse the continuation game into a single period game. • Conceptually, collusion games are equivalent to a single shot oligopoly game followed by a single shot coordination game. • Collusion requires coordination on history contingent strategies.

10. Two Stage Bertrand Game • To implement the game, we chose parameters such that collusion at high prices can only be supported using the harshest possible punishment (coordination on low prices) and that coordination at (M,M) is the risk dominant equilibrium in the second period. • We set πL = 78, πM = 138, and πH = 168. • The discount rate is δ = 2/3. • To sharpen the incentives, a fixed cost of 24 was subtracted from all payoffs.

11. The Two Stage Collusion Game L M H L Period 1 M H

12. The Risk Dominant Outcome The Two Stage Collusion Game Period 2

13. The Two Stage Collusion Game L M H L M H

14. Advantages of a Two Stage Game • Similar approaches in Holt and Davis, 1999; Andersson and Wengström, 2007. • Longer games allow for richer interactions and make the relationship between periods more clear. Nonetheless, using the two stage game has several advantages. • We are interested in learning. Using a two stage game allows for a large number of repetitions without many “wasted” rounds (e.g. only one game played) or excessive variation in payoffs (Bereby-Myers and Roth, 2006). Either would slow learning. • Reduces complexity of the strategy and message spaces. • Eases econometric analysis of the data. • Reduces the importance of risk preferences.

15. Experimental Design • Subjects in all sessions play twenty rounds of the TSBG. • First ten rounds have no communication. • Communication is introduced for the second half of the experiment. The form of communication is a treatment variable. • Subjects are in large sessions (at least twenty subjects) and random rematching is used to reduce repeated game effects between rounds. • All subjects were undergraduates at CWRU. Sessions took 75 – 105 minutes – sessions with more communication took longer. All sessions were run using CWRU’s mobile lab. Software is programmed in z-tree (Fischbacher, 2007). • The conversion rate was 130 ECU/$. There was a show-up fee of $6. Subjects are paid for all rounds. Average pay was slightly below $20/subject.

16. Messages • Fixed Messages – each subject sends a single message simultaneously. Very limited message space is available. Subject have option of send no message or a partial message. • First period message • “I think we should choose the following in Period 1” • Specify my choice and other’s choice • Contingencies • Communicated at the same time as first period message • Second period choices, conditioned on whether both played according to first period recommendation • Second period message • Analogous to first period messages • Subjects know full first period history

17. Chat • Using latest version of z-tree (Fischbacher, 2007), we allow unstructured chat prior to the first and/or second periods. • Subjects are only instructed to not identify themselves and to avoid offensive language. • Allows for better coordination of choices and richer communication. • Subjects were allowed 75 seconds to chat. They were instructed to “sign off” when making a decision.

18. Experimental Design

19. Results: Message Treatments • Treatment Effects on Cooperation • Adding first period messages improves collusion. This effect is largely transient, although there is still significantly more collusion in late periods than with no messages. • Allowing contingencies only slightly improves collusion initially, but less deterioration occurs with experience. • Allowing second period messages has no obvious effect on either the initial improvement in collusion or on the deterioration over time. • This clarifies an ambiguous result from Andersson and Wengström, 2007. • Allowing second period communication does improve coordination in the second period. • The difference in early periods between the First Period Only treatment and the two treatments with contingencies is only weakly significant. In late rounds, the two treatments with contingencies lead to significantly higher collusion, but there is not a significant difference between the two treatments.

20. Results: Collusion in Message Treatments

21. Results: Second Period Coordination

22. Results: What’s in the Messages • Subjects almost always send a message (96% of all observations). • Usage of contingent messages is common but certainly not pervasive. • Only 51% of subjects ever send a contingent message. • Lower usage of contingent messages in treatment with second period messages is consistent with renegotiation stories. • Unambiguous lying is quite common. • In observations where an unambiguous lie can be identified (e.g. both players said they would cooperate), 50% of all observations are unambiguous lies. • Unambiguous lies increase in frequency with experience. • Unambiguous lies are less common, especially in early rounds, for treatments with contingent messages. This difference is statistically significant in early rounds.

23. Results: Use of Contingent Messages

24. Results: Frequency of Unambiguous Lies

25. Do the Messages Matter? • Subjects respond strongly to messages about intended first period actions. • This is unsurprising – if you say you won’t cooperate, why should I? • Sending no message is just as bad. • Contingent messages matter slightly, but only in a negative way. • If you threaten to punish people, it makes them slightly less likely to cooperate. • This effect gets much stronger in later rounds. • Lying has a strong negative effect on cooperation. • This effects gets slightly stronger in later rounds. • Only explains about 15% of difference between contingency and non-contingency treatments.

26. Linear Probability Model:Effect of Messages on Period 1 Cooperation

27. So Why Do Contingencies Matter? • Subjects may not send messages about contingent behavior, but they certainly act in a contingent fashion. • There is strong positive correlation between first period cooperation by the other player and second period cooperation. • This correlation does not significantly differ across the four treatments. • One possibility is that having to send a message about the second period makes subjects think more about the second period.

28. Results: Chat • Allowing first period chat leads to dramatically higher levels of collusion. There is no deterioration in collusion with experience. • There is a slight dip in the middle periods. • Coordination slightly improves in the second period. • Adding second period chat substantially improves collusion. Collusion slightly improves with experience. • This directly contradicts the relevant theory of renegotiation. • There is also improvement in second period coordination with second period chat.

29. Results: First Period Choices with Chat

30. Results: Second Period Choices with Chat

31. Content Analysis • All messages were coded for content. • David and I separately developed coding schemes for a test sample of messages. • We then reconciled our separate coding schemes into a single unified set of codes. • Two RAs were independently trained and independently coded all messages. • The coding is binary. Coders were free to choose as many or few codes as they desired. Coders were not told anything about our hypotheses for the data. • The cross-coder correlations for major categories (with one exception) are pretty good – always at least .5 and usually around .7 or .8. Cross-coder correlations around .6 for major categories are what we’ve typically seen in earlier studies. • Data reported below is based on whether the category was coded by either coder during a conversation.

32. What is Important in Chat?

33. Most Common Period 1 Codes

34. Most Common Period 2 Codes

35. Linear Probability Model:Effect of Chat on First Period Cooperation