Testing Models of Strategic Uncertainty: Equilibrium Selection in Repeated Games

Abstract

In repeated games, where both collusive and non-collusive outcomes can be supported as equilibria, it is crucial to understand the likelihood of selection for each type of equilibrium. Controlled experiments have empirically validated a selection criterion for the two-player repeated prisoner’s dilemma: the basin of attraction for always defect. This prediction device uses the game primitives to measure the set of beliefs for which an agent would prefer to unconditionally defect rather than attempt conditional cooperation. This belief measure reflects strategic uncertainty over others’ actions, where the prediction is for non-cooperative outcomes when the basin measure is full, and cooperative outcomes when empty. We expand this selection notion to multi-player social dilemmas and experimentally test the predictions, manipulating both the total number of players and the payoff tensions. Our results affirm the model as a tool for predicting long-term cooperation while also speaking to some limitations when dealing with first-time encounters.