Asymmetric Equilibria in Symmetric Multiplayer Prisoners Dilemma Supergames

TL;DR

This paper introduces a finite automaton-based solution concept for supergames, demonstrating the existence of symmetric and asymmetric equilibria in symmetric multiplayer prisoners' dilemma supergames under certain conditions.

Contribution

It proposes a novel automaton-style equilibrium concept for supergames and characterizes conditions for the existence of symmetric and asymmetric equilibria.

Findings

Supergames contain at least one symmetric equilibrium.

Asymmetric equilibria can also exist under certain conditions.

The model applies to locally non-cooperative stage games with decreasing utility functions.

Abstract

We propose a finite automaton-style solution concept for supergames. In our model, we define an equilibrium to be a cycle of state switches and a supergame to be an infinite walk on states of a finite stage game. We show that if the stage game is locally non-cooperative, and the utility function is monotonously decreasing as the number of defective agents increases, the symmetric multiagent prisoners' dilemma supergame must contain one symmetric equilibrium and can contain asymmetric equilibria.