Optimal Correlated Equilibria in General-Sum Extensive-Form Games: Fixed-Parameter Algorithms, Hardness, and Two-Sided Column-Generation

TL;DR

This paper introduces fixed-parameter algorithms and a two-sided column-generation method for computing optimal correlated equilibria in extensive-form games, addressing complexity challenges and improving computational efficiency.

Contribution

It presents a new fixed-parameter algorithm for various correlated equilibria and a two-sided column-generation approach that outperforms previous methods.

Findings

Algorithms run efficiently when the information structure parameter is small.

Proved complexity gaps for certain equilibrium concepts.

Experimental results show improved performance over prior methods.

Abstract

We study the problem of finding optimal correlated equilibria of various sorts in extensive-form games: normal-form coarse correlated equilibrium (NFCCE), extensive-form coarse correlated equilibrium (EFCCE), and extensive-form correlated equilibrium (EFCE). We make two primary contributions. First, we introduce a new algorithm for computing optimal equilibria in all three notions. Its runtime depends exponentially only on a parameter related to the information structure of the game. We also prove a fundamental complexity gap: while our size bounds for NFCCE are similar to those achieved in the case of team games by Zhang et al., this is impossible to achieve for the other two concepts under standard complexity assumptions. Second, we propose a two-sided column generation approach for use when the runtime or memory usage of the previous algorithm is prohibitive. Our algorithm improves upon the one-sided approach of Farina et al. by means of a new decomposition of correlated strategies which allows players to re-optimize their sequence-form strategies with respect to correlation plans which were previously added to the support. Experiments show that our techniques outperform the prior state of the art for computing optimal general-sum correlated equilibria.