A Shapley Value Representation of Potential Games

the University of Tokyo. Special thanks are due to Hideshi Itoh for suggesting the application to contract theory during the seminar at Osaka University. The usual disclaimer applies. Abstract: In potential games, as considered by Monderer and Shapley (1996a), 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) of cooperative games indexed by the strategy set. Section 2 Γ = (N, A, u): a strategic form game.