Cooperation in the repeated prisoner's dilemma game with local interaction and local communication

Abstract

This paper considers a repeated prisoner's dilemma game in a network in which each agent interacts with his neighbors and cannot observe the actions of other agents who are not directly connected to him. If there is global information processing through public randomization and global communication, it is not difficult to construct a sequential equilibrium which supports cooperation and satisfies a property, called stability, which requires that cooperation resumes after any history. In this paper, we allow agents to locally communicate with their neighbors and show that it is possible to construct such an equilibrium without global information processing. Here, the role of local communication is to resolve the discrepancy of agents’ expectations about their neighbor's future actions.

Efficiency in repeated games with local interaction and uncertain local monitoring

“…Haag and Lagunoff (2006) consider games with prisoner's dilemma interactions and heterogeneous discount rates, and show for which monitoring structures cooperation can be sustained by local trigger strategies. Xue (2004) and Cho (2011Cho ( , 2013 also focus on the prisoner's dilemma. Cho (2013) considers acyclical networks and allows neighbors to communicate.…”

“…Xue (2004) and Cho (2011Cho ( , 2013 also focus on the prisoner's dilemma. Cho (2013) considers acyclical networks and allows neighbors to communicate. Cho (2011) shows the existence of sequential equilibria in which players cooperate in every period and in which cooperation eventually resumes after deviations if public randomization is allowed.…”

Communication in repeated network games with imperfect monitoring

“…Hence, the deviations of players 1 and 3 induce the same distribution of payoffs for player 2, and that for every strategy (possibly mixed) of the non-deviating players. 7 Hence, player 2 cannot infer the identity of the deviator from the observation of his payoffs. Second, neither player 4 nor player 5 has relevant information on the actions chosen by players 1 and 3.…”

“…each player observes his neighbors' moves) but communication is constrained by the network structure (they also establish a necessary and sufficient condition for a folk theorem to hold). All these papers [5,29,34] (and also [7,22,26,35]) assume that monitoring among neighbors is perfect. To the contrary, I assume here that it is imperfect: payoffs encapsulate all an agent's feedback about his neighbors' play (for instance, firms infer rivals' likely behavior from their own profits).…”

Social norms and cooperation

“…1 I establish that there exists an equilibrium outcome where cooperation exists. The cooperation does not rely on repeated play (Chen 2010), communication (Cho 2014), or any external institutional mechanism such as punishment (Hilbe et al 2015). Psychological game theory can explain cooperative behavior.…”