Games With Tolerant Players

A notion of π-tolerant equilibrium is defined that takes into account that players have some tolerance regarding payoffs in a game. This solution concept generalizes Nash and refines ε-Nash equilibrium in a natural way. We show that π-tolerant equilibrium can explain cooperation in social dilemmas such as Prisoner’s Dilemma and the Public Good game. We then examine the structure of particularly cooperative π-tolerant equilibria, where players are as cooperative as they can be, subject to their tolerances, in Prisoner’s Dilemma. To the extent that cooperation is due to tolerance, these results provide guidance to a mechanism designer who has some control over the payoffs in a game, and suggest ways in which cooperation can be increased.