A projection framework for near-potential games

Abstract

Potential games are a special class of games that admit tractable static and dynamic analysis. Intuitively, games that are “close” to a potential game should enjoy somewhat similar properties. This paper formalizes and develops this idea, by introducing a systematic framework for finding potential games that are close to a given arbitrary strategic-form finite game. We show that the sets of exact and weighted potential games (with fixed weights) are subspaces of the space of games, and that for a given game, the closest potential game in these subspaces (possibly subject to additional constraints) can be found using convex optimization. We provide closed-form solutions for the closest potential game in these subspaces, and extend our framework to more general classes of games. We further investigate and quantify to what extent the static and dynamic features of potential games extend to “near-potential” games. In particular, we show that for a given strategic-form game, we can characterize the approximate equilibria and the sets to which better-response dynamics converges, as a function of the distance of the game to its potential approximation.