Statistical physics approach to graphical games: local and global interactions

TL;DR

This paper applies statistical physics, specifically the cavity method, to analyze the structure of equilibria in graphical games with local and global interactions, and proposes a distributed algorithm for finding pure Nash equilibria.

Contribution

It introduces a new representation for graphical games that handles both local and global interactions and applies the cavity method to study equilibrium space structure.

Findings

Provides a geometrical analysis of equilibrium sets.

Develops a local, distributive algorithm for pure Nash equilibria.

Extends methods to approximate mixed Nash equilibria.

Abstract

In a graphical game agents play with their neighbors on a graph to achieve an appropriate state of equilibrium. Here relevant problems are characterizing the equilibrium set and discovering efficient algorithms to find such an equilibrium (solution). We consider a representation of games that extends over graphical games to deal conveniently with both local a global interactions and use the cavity method of statistical physics to study the geometrical structure of the equilibria space. The method also provides a distributive and local algorithm to find an equilibrium. For simplicity we consider only pure Nash equilibria but the methods can as well be extended to deal with (approximated) mixed Nash equilirbia.