Reciprocity with uncertainty about others

We introduce the uncertainty of psychological motivation into a reciprocity model and explore its implications on behavior. More precisely, we assume that reciprocity sensitivities are subject to incomplete information and extend the Sequential Reciprocity Equilibrium in extensive-form games (Dufwenberg and Kirchsteiger, 2004) to a broader class of incomplete information games. We use this general framework to study many well-known games and find that uncertainty could either mitigate or strengthen players' reciprocal behavior. We investigate how uncertainty changes the equilibrium predictions of the standard reciprocity model and compare two setups in which the psychological motivations are known and unknown among the players, respectively. In particular, we find that, in the prisoners' dilemma, players are more likely to cooperate with each other when they have information about the reciprocal motivations of their opponents, given that the benefits of defection are modest.