On the Communication Complexity of Approximate Nash Equilibria
We study the problem of computing approximate Nash equilibria, in a setting where players initially know their own payoffs but not the payoffs of other players. In order for a solution of reasonable quality to be found, some amount of communication needs to take place between the players. We are interested in algorithms where the communication is substantially less than the contents of a payoff matrix, for example logarithmic in the size of the matrix. At one extreme is the case where the players do not communicate at all; for this case (with 2 players having n×n matrices) ε-Nash equilibria can be computed for ε = 3/4, while there is a lower bound of slightly more than 1/2 on the lowest ε achievable. When the communication is polylogarithmic in n, we show how to obtain ε = 0.438. For one-way communication we show that ε = 1/2 is the exact answer.
KeywordsNash Equilibrium Mixed Strategy Pure Strategy Communication Complexity Nash Equilibrium Strategy
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