Congestion Games with Player-Specific Payoff Functions
Games and Economic Behavior 13 (1996), 111–124
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 tobest-reply strategiesmay be cyclic. But there is always at least one such path that connects an arbitrary initial point to an equilibrium.