A Shapley Value Representation of Potential Games

Abstract

In potential games, as considered by Monderer and Shapley (1996a, Games Econom. Behav.14, 124-143), each player's gain from a deviation is equal to the gain in a potential function. We prove that a game has a potential function if and only if its payoff functions coincide with the Shapley value of a particular class of cooperative games indexed by the set of strategy profiles. Also a potential function of a noncooperative potential game coincides with the potentials (cf. Hart and Mas-Colell, 1989, Econometrica57, 589-614) of cooperative games indexed by the strategy set. Journal of Economic Literature Classification Numbers: C71, C72. © 2000 Academic Press.