Coarse Correlation in Extensive-Form Games
This work addresses a gap in game theory for researchers and practitioners by extending coarse correlation concepts to extensive-form settings, though it is incremental as it builds on classical ideas.
The paper tackles the problem of coarse correlation in extensive-form games by introducing the new concept of extensive-form coarse-correlated equilibrium (EFCCE) and comparing it to existing equilibria, showing that social-welfare-maximizing EFCCEs and NFCCEs are bilinear saddle points and providing an algorithm for NFCCE that is two to four orders of magnitude faster than prior methods.
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.