Congestion games with player-specific payoff functions

A class of noncooperative games in which the players share a common set of strategies is described. The payoff a player receives for playing a particular strategy depends only on the total number of players playing the same strategy and decreases with that number in a manner which is specific to the particular player. It is shown that each game in this class possesses at least one Nash equilibrium in pure strategies. Best-reply paths in which players, one at a time, shift to best-reply strategies may be cyclic. But there is always at least one such path that connects an arbitrary initial point to an equilibrium. Journal of Economic Literature Classification Number: C72.