Coarse Correlation in Extensive-Form Games

TL;DR

This paper explores coarse correlation concepts in extensive-form games, introduces a new equilibrium type, and presents efficient algorithms with significant speed improvements over previous methods.

Contribution

It introduces the extensive-form coarse-correlated equilibrium (EFCCE), analyzes its relation to existing equilibria, and develops faster algorithms for computing these equilibria.

Findings

EFCCE is a subset of NFCCE and a superset of the extensive-form correlated equilibrium.

Social-welfare-maximizing EFCCEs and NFCEEs are bilinear saddle points.

Proposed algorithms are 100 to 10,000 times faster than previous methods.

Abstract

Coarse correlation models strategic interactions of rational agents complemented by a correlation device, that is a mediator that can recommend behavior but not enforce it. Despite being a classical concept in the theory of normal-form games for more than forty years, not much is known about the merits of coarse correlation in extensive-form settings. In this paper, we consider two instantiations of the idea of coarse correlation in extensive-form games: normal-form coarse-correlated equilibrium (NFCCE), already defined in the literature, and extensive-form coarse-correlated equilibrium (EFCCE), which we introduce for the first time. We show that EFCCE is a subset of NFCCE and a superset of the related extensive-form correlated equilibrium. We also show that, in two-player extensive-form games, social-welfare-maximizing EFCCEs and NFCEEs are bilinear saddle points, and give new efficient algorithms for the special case of games with no chance moves. In our experiments, our proposed algorithm for NFCCE is two to four orders of magnitude faster than the prior state of the art.