Exchangeable Equilibria, Part I: Symmetric Bimatrix Games

TL;DR

This paper introduces exchangeable equilibria in symmetric bimatrix games, a new class of correlated equilibria with players' strategies conditionally i.i.d., which can outperform symmetric Nash equilibria in expected utility.

Contribution

It defines exchangeable equilibria, explores their properties, and establishes their relationship with symmetric Nash and correlated equilibria, including a geometric and interpretative analysis.

Findings

Exchangeable equilibria form a convex set.

They can yield higher expected utility than symmetric Nash equilibria.

The set lies between symmetric Nash and correlated equilibria.

Abstract

We introduce the notion of exchangeable equilibria of a symmetric bimatrix game, defined as those correlated equilibria in which players' strategy choices are conditionally independently and identically distributed given some hidden variable. We give several game-theoretic interpretations and a version of the "revelation principle". Geometrically, the set of exchangeable equilibria is convex and lies between the symmetric Nash equilibria and the symmetric correlated equilibria. Exchangeable equilibria can achieve higher expected utility than symmetric Nash equilibria.