A projection framework for near-potential polynomial games

It has been shown that in the case of finite games, games with a small Maximum Pairwise Difference (MPD) to a potential game share some of their favorable static and dynamic characteristics. In this paper, we extend these results to games in which strategy sets can be either finite, or closed intervals of the real line; and utility functions are polynomials in the players' actions. We define a notion of distance in the space of polynomial games in terms of the Maximum Differential Difference (MDD) between two games, and relate this concept to their MPD. We also show that a nearby polynomial potential game can be obtained from the solution of a semidefinite program. We then use polynomial potential games to study the static and dynamic properties of nearby polynomial games. In particular, we relate the approximate equilibria and approximate better response dynamics of a polynomial game to those of a nearby polynomial potential game in terms of their MDD.