Polynomial stochastic games via sum of squares optimization

TL;DR

This paper introduces a method to compute equilibria in polynomial stochastic games with a single-controller assumption using semidefinite programming, extending solution techniques for complex game scenarios.

Contribution

It develops a novel approach to solve polynomial stochastic games with single-controller assumption through sum of squares optimization and semidefinite programming.

Findings

Minimax equilibria can be computed efficiently for the specified class.

Optimal strategies are derived using semidefinite programming techniques.

The approach extends to infinite strategy spaces with polynomial payoffs.

Abstract

Stochastic games are an important class of problems that generalize Markov decision processes to game theoretic scenarios. We consider finite state two-player zero-sum stochastic games over an infinite time horizon with discounted rewards. The players are assumed to have infinite strategy spaces and the payoffs are assumed to be polynomials. In this paper we restrict our attention to a special class of games for which the single-controller assumption holds. It is shown that minimax equilibria and optimal strategies for such games may be obtained via semidefinite programming.