An epistemic approach to explaining cooperation in the finitely repeated Prisoner\u2019s Dilemma

Abstract

We use epistemic game theory to explore rationales behind cooperative behaviors in the finitely repeated Prisoner’s Dilemma. For a class of type structures that are sufficiently rich, the set of outcomes that can arise when each player i is rational and satisfies (m_i-1)th order strong belief of rationality is the set of paths on which each player i defects in the last m_i rounds. We construct one sufficiently rich type structure to elaborate on how different patterns of cooperative behaviors arise under sufficiently weak epistemic conditions. In this type structure, the optimality of forgiving the opponent’s past defection and the belief that one’s defection will be forgiven account for the richness of the set of behavior outcomes.