The complexity of approximate (coarse) correlated equilibrium for incomplete information games

• URL: http://arxiv.org/abs/2406.02357v1
• Date: Tue, 4 Jun 2024 14:35:27 GMT
• Title: The complexity of approximate (coarse) correlated equilibrium for incomplete information games
• Authors: Binghui Peng, Aviad Rubinstein,
• Abstract summary: We study the complexity of decentralized learning of approximate correlated equilibria in incomplete information games. Our lower bound holds even for the easier solution concept of $epsilon$-approximate $mathitco$ correlated equilibrium.
• Score: 16.96984593866157
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the iteration complexity of decentralized learning of approximate correlated equilibria in incomplete information games. On the negative side, we prove that in $\mathit{extensive}$-$\mathit{form}$ $\mathit{games}$, assuming $\mathsf{PPAD} \not\subset \mathsf{TIME}(n^{\mathsf{polylog}(n)})$, any polynomial-time learning algorithms must take at least $2^{\log_2^{1-o(1)}(|\mathcal{I}|)}$ iterations to converge to the set of $\epsilon$-approximate correlated equilibrium, where $|\mathcal{I}|$ is the number of nodes in the game and $\epsilon > 0$ is an absolute constant. This nearly matches, up to the $o(1)$ term, the algorithms of [PR'24, DDFG'24] for learning $\epsilon$-approximate correlated equilibrium, and resolves an open question of Anagnostides, Kalavasis, Sandholm, and Zampetakis [AKSZ'24]. Our lower bound holds even for the easier solution concept of $\epsilon$-approximate $\mathit{coarse}$ correlated equilibrium On the positive side, we give uncoupled dynamics that reach $\epsilon$-approximate correlated equilibria of a $\mathit{Bayesian}$ $\mathit{game}$ in polylogarithmic iterations, without any dependence of the number of types. This demonstrates a separation between Bayesian games and extensive-form games.

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