A Simple Adaptive Procedure Converging to Forgiving Correlated Equilibria

TL;DR

This paper introduces a simple, decentralized adaptive method for extensive-form games that converges to forgiving correlated equilibria, a refined solution concept encouraging consistent player recommendations based on information sets.

Contribution

It extends normal-form regret minimization techniques to extensive-form games, enabling convergence to forgiving correlated equilibria with minimal information requirements.

Findings

Procedure converges to forgiving correlated equilibria.

Players follow recommendations based on local information.

Method is fully decentralized and scalable.

Abstract

Simple adaptive procedures that converge to correlated equilibria are known to exist for normal form games (Hart and Mas-Colell 2000), but no such analogue exists for extensive-form games. Leveraging inspiration from Zinkevich et al. (2008), we show that any internal regret minimization procedure designed for normal-form games can be efficiently extended to finite extensive-form games of perfect recall. Our procedure converges to the set of forgiving correlated equilibria, a refinement of various other proposed extensions of the correlated equilibrium solution concept to extensive-form games (Forges 1986a; Forges 1986b; von Stengel and Forges 2008). In a forgiving correlated equilibrium, players receive move recommendations only upon reaching the relevant information set instead of all at once at the beginning of the game. Assuming all other players follow their recommendations, each player is incentivized to follow her recommendations regardless of whether she has done so at previous infosets. The resulting procedure is completely decentralized: players need neither knowledge of their opponents' actions nor even a complete understanding of the game itself beyond their own payoffs and strategies.