Simple Recursive Games

TL;DR

This paper introduces simple recursive games, a class of stochastic games without chance moves, and presents an almost-linear time algorithm for computing their equilibrium, advancing understanding of their computational complexity.

Contribution

It defines simple recursive games and develops an almost-linear time comparison-based algorithm for finding their equilibrium, addressing a key open problem.

Findings

Developed an almost-linear time algorithm for simple recursive games.

Proved the existence of an equilibrium can be computed efficiently.

Open problem remains for linear time comparison-based algorithms.

Abstract

We define the class of "simple recursive games". A simple recursive game is defined as a simple stochastic game (a notion due to Anne Condon), except that we allow arbitrary real payoffs but disallow moves of chance. We study the complexity of solving simple recursive games and obtain an almost-linear time comparison-based algorithm for computing an equilibrium of such a game. The existence of a linear time comparison-based algorithm remains an open problem.