The Value of Recall in Extensive-Form Games

TL;DR

This paper investigates the value of perfect recall in imperfect-recall extensive-form games, quantifying its benefits, complexities, and limitations, and connecting it to broader game theory concepts like the price of anarchy.

Contribution

It introduces the concept of value of recall (VoR), analyzes its bounds and pathologies, studies its computational complexity, and links it to existing game theory frameworks.

Findings

VoR can be unbounded but is parameterized by game properties

Identifies pathologies and methods to circumvent them

Connects VoR to the price of anarchy and smoothness framework

Abstract

Imperfect-recall games, in which players may forget previously acquired information, have found many practical applications, ranging from game abstractions to team games and testing AI agents. In this paper, we quantify the utility gain by endowing a player with perfect recall, which we call the value of recall (VoR). While VoR can be unbounded in general, we parameterize it in terms of various game properties, namely the structure of chance nodes and the degree of absentmindedness (the number of successive times a player enters the same information set). Further, we identify several pathologies that arise with VoR, and show how to circumvent them. We also study the complexity of computing VoR, and how to optimally apportion partial recall. Finally, we connect VoR to other previously studied concepts in game theory, including the price of anarchy. We use that connection in conjunction with the celebrated smoothness framework to characterize VoR in a broad class of games.