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 $N \times N$ 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.

中文翻译：

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潜在博弈中纳什均衡的通信复杂度

我们证明了潜在博弈中（可能是混合的）纳什均衡的通信复杂度下限。特别是，我们证明了找到纳什均衡需要在两人 $N \times N$ 个潜在博弈中的 $poly(N)$ 交流，以及 $n$-玩家两人中的 $2^{poly(n)}$ 交流-动作类游戏。据我们所知，这些是在潜在博弈中（可能是混合的）纳什均衡的任何模型中证明硬度的第一个结果。