Signaling and tacit collusion in an infinitely repeated Prisoners’ Dilemma

In 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.