Games With Tolerant Players

TL;DR

This paper introduces pi-tolerant equilibrium, a new solution concept that accounts for players' payoff tolerances, explaining cooperation in social dilemmas and guiding mechanisms to enhance cooperation.

Contribution

It defines pi-tolerant equilibrium, generalizes Nash and epsilon-Nash, and analyzes highly cooperative equilibria influenced by players' tolerances.

Findings

Pi-tolerant equilibrium explains cooperation in social dilemmas.

Cooperative equilibria are characterized by players' tolerances.

Results suggest mechanisms to increase cooperation by adjusting payoffs.

Abstract

A notion of pi-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 epsilon-Nash equilibrium in a natural way. We show that pi-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 pi-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.