Communication complexity of Nash equilibrium in potential games
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We prove communication complexity lower bounds for (possibly mixed) Nash equilibrium in potential games. In particular, we show that finding a Nash equilibrium requires poly(N) communication in two-player N × N potential games, and 2^poly(n) communication in n-player two-action games. To the best of our knowledge, these are the first results to demonstrate hardness in any model of (possibly mixed) Nash equilibrium in potential games.
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