Generic Uniqueness of Equilibria in Nonatomic Congestion Games

Igal Milchtaich

Generic uniqueness of pure-strategy Nash equilibrium, and uniqueness of the equilibrium outcome, are proved for a class of noncooperative nonatomic (large) games where a player's payoff depends on, and strictly decreases with, the measure of the set of players playing the same (pure) strategy he is playing. If the play of mixed strategies is allowed, then similar results still hold when the assumption of nonatomicity of the measure is removed. Generic uniqueness of the Cournot-Nash equilibrium distribution, corresponding to a description of a game in terms of distribution of player types, is also proved.

January, 1996
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