Stochastic Limit-Average Games are in EXPTIME

TL;DR

This paper proves that computing the approximate value of finite-state two-player zero-sum stochastic limit-average games can be done within exponential time, providing complexity bounds for these types of games.

Contribution

It establishes that stochastic limit-average games are in EXPTIME, offering a complexity classification for their approximation problem.

Findings

Approximate values can be computed in exponential time.

Provides bounds on the computational complexity of stochastic limit-average games.

Results apply to all positive approximation precisions.

Abstract

The value of a finite-state two-player zero-sum stochastic game with limit-average payoff can be approximated to within $\epsilon$ in time exponential in a polynomial in the size of the game times polynomial in logarithmic in $\frac{1}{\epsilon}$, for all $\epsilon>0$.