The Communication Complexity of Uncoupled Nash Equilibrium Procedures
Srgiu Hart and Yishay Mansour
In: STOC 2007, June 8-16, 2007, San Diego, CA.

Abstract

We study the question of how long it takes players to reach a Nash equilibrium in uncoupled setups, where each player initially knows only his own payo® function. We derive lower bounds on the communication complexity of reaching a Nash equilibrium, i.e., on the number of bits that need to be transmitted, and thus also on the required number of steps. Speci¯cally, we show lower bounds that are exponential in the number of players in each one of the following cases: (1) reaching a pure Nash equilibrium; (2) reaching a pure Nash equilibrium in a Bayesian setting; and (3) reaching a mixed Nash equilibrium. We then show that, in contrast, the com- munication complexity of reaching a correlated equilibrium is polynomial in the number of players.

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