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Communication complexity of Nash equilibrium in potential games
arXiv - CS - Computational Complexity Pub Date : 2020-11-12 , DOI: arxiv-2011.06660
Yakov Babichenko and Aviad Rubinstein

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:

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。
更新日期:2020-11-16
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