Imperfect-Recall Games: Equilibrium Concepts and Their Complexity

TL;DR

This paper explores the computational complexity of finding equilibria in multiplayer extensive-form games with imperfect recall, analyzing various solution concepts and special cases.

Contribution

It provides a comprehensive complexity analysis of equilibrium computation in imperfect-recall games across multiple solution concepts and game settings.

Findings

Complexity results vary across solution concepts and game types.

Certain cases are shown to be computationally hard, relating to known complexity classes.

The analysis includes both exact and approximate equilibrium computation.

Abstract

We investigate optimal decision making under imperfect recall, that is, when an agent forgets information it once held before. An example is the absentminded driver game, as well as team games in which the members have limited communication capabilities. In the framework of extensive-form games with imperfect recall, we analyze the computational complexities of finding equilibria in multiplayer settings across three different solution concepts: Nash, multiselves based on evidential decision theory (EDT), and multiselves based on causal decision theory (CDT). We are interested in both exact and approximate solution computation. As special cases, we consider (1) single-player games, (2) two-player zero-sum games and relationships to maximin values, and (3) games without exogenous stochasticity (chance nodes). We relate these problems to the complexity classes P, PPAD, PLS, $\Sigma_2^P$ , $\exists$R, and $\exists \forall$R.