Signaling and tacit collusion in an infinitely repeated Prisoners’ Dilemma

Abstract

a b s t r a c tIn the context of an infinitely repeated Prisoners' Dilemma, we explore how cooperation is initiated when players signal and coordinate through their actions. There are two types of players -patient and impatient -and a player's type is private information. An impatient type is incapable of cooperative play, while if both players are patient types -and this is common knowledge -then they can cooperate with a grim trigger strategy. We find that the longer that players have gone without cooperating, the lower is the probability that they will cooperate in the next period. While the probability of cooperation emerging is always positive, there is a positive probability that cooperation never occurs.

Antitrust as Facilitating Factor for Collusion

“…This explanation is also pointed out byHarrington(2004) andWhinston (2006, p. 32) 6. See, for example,Motta (2004),Whinston (2006),Martin (2006) andDavies and Olczak (2008) 7.…”

“…In recent years, there is a growing interest in the distinction between the economic and legal approach to industrial collusion. 6 Whereas economists generally do not distinguish between tacit and explicit collusion, lawyers require that firms have reached an agreement on one or more key strategic variables (e.g., prices or outputs). 7 Therefore, in order to better guide antitrust enforcement, it is of importance to improve our understanding of when and why conspirators communicate directly rather than through the market.…”

“…To avoid this risk of losing business, it can alternatively wait in the hope that its rival will initiate collusion. Harrington and Zhao (2012) find that in this case it might take long before firms reach a collusive agreement and that they may not reach an agreement at all. This finding raises the question of whether firms can do a better job by colluding explicitly.…”

“…Recently, Harrington and Zhao (2012) have shown that tacit collusion can be quite a challenge for firms that have incomplete knowledge about each other's intentions to collude. Specifically, they study an infinitely repeated prisoners' dilemma in which discount factors are private information.…”

A theory of collusion with partial mutual understanding

“…For example, a …rm could believe that another …rm will always act as a price leader or instead that other -as a …rm raises its price before others do -each …rm would like another …rm to lead which could generate miscoordination. Consistent with this view, equilibrium analyses show that "a leaderfollower pattern where a single …rm consistently leads all price changes is unlikely" (Pastine and Pastine, 2004, p. 136) and there is delay in price leadership because each …rm waits for the other to take the lead (Harrington and Zhao, 2012). …rms believe it'll be the price leader.…”