A Shapley value representation of potential games

In potential games, as considered by Monderer and Shapley (1996a, Games Eco nom. Behav. 14, 124-143), each player's gain from a deviation is equal to t he gain in a potential function. We prove that a game has a potential funct ion 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 prof iles. Also a potential function of a noncooperative potential game coincide s with the potentials (cf. Hart and Mas-Colell, 1989, Econometrica 57, 589- 614) of cooperative games indexed by the strategy set. Journal of Economic Literature Classification Numbers: C71, C72. (C) 2000 Academic Press (C) 20 00 Academic Press.