Graphical potential games

TL;DR

This paper characterizes graphical potential games as equivalent to Markov random fields on a graph, enabling local potential decomposition and bounding strategy changes, with extensions to infinite graphs.

Contribution

It establishes a novel equivalence between graphical potential games and Markov random fields, allowing local potential decomposition and analysis of strategy dynamics.

Findings

Potential functions decompose into local potentials.

Bound on the number of strategy changes along better response paths.

Extension of results to infinite graphs.

Abstract

We study the class of potential games that are also graphical games with respect to a given graph $G$ of connections between the players. We show that, up to strategic equivalence, this class of games can be identified with the set of Markov random fields on $G$. From this characterization, and from the Hammersley-Clifford theorem, it follows that the potentials of such games can be decomposed to local potentials. We use this decomposition to strongly bound the number of strategy changes of a single player along a better response path. This result extends to generalized graphical potential games, which are played on infinite graphs.