New algorithms for solving stochastic games

TL;DR

This paper introduces new algorithms that efficiently compute exact discounted values and game values in stochastic games, significantly improving upon previous methods in terms of computational complexity.

Contribution

It provides polynomial-time algorithms for calculating exact solutions in stochastic games, surpassing the efficiency of prior algorithms.

Findings

Algorithms are polynomial in the number of pure stationary strategies.

The new algorithms improve upon the most efficient previous methods.

Exact expressions for discounted values and the game value are computable.

Abstract

Stochastic games are a classical model in game theory in which two opponents interact and the environment changes in response to the players' behavior. The central solution concepts for these games are the discounted values and the value, which represent what playing the game is worth to the players for different levels of impatience. In the present manuscript, we provide algorithms for computing exact expressions for the discounted values and for the value, which are polynomial in the number of pure stationary strategies of the players. This result considerably improves all the existing algorithms, including the most efficient one, due to Hansen, Kouck\'y, Lauritzen, Miltersen and Tsigaridas (STOC 2011).