The communication complexity of uncoupled nash equilibrium procedures

We study the question of how long it takes players to reach a Nashequilibrium in uncoupled setups, where each player initially knowsonly his own payoff function. We derive lower bounds on the communication complexity of reaching a Nash equilibrium, i.e., on thenumber of bits that need to be transmitted, and thus also on the requirednumber of steps. Specifically, we show lower bounds that are exponential inthe number of players in each one of the following cases: (1) reaching apure Nash equilibrium; (2) reaching a pure Nash equilibrium in a Bayesiansetting; and (3) reaching a mixed Nash equilibrium. We then show that, incontrast, the communication complexity of reaching a correlated equilibriumis polynomial in the number of players.