On Zero-Sum Two Person Perfect Information Stochastic Games

TL;DR

This paper proves the existence of optimal pure stationary strategies in zero-sum two-player perfect information stochastic games with average payoff, and provides a finite-step algorithm to compute them.

Contribution

It establishes the existence of pure stationary strategies and introduces a finite-step algorithm for their computation in PISGs.

Findings

Existence of a game value and optimal pure stationary strategies.

The payoff matrix has a pure saddle point.

A finite-step algorithm for strategy computation.

Abstract

A zero-sum two person Perfect Information Stochastic game (PISG) under limiting average payoff has a value and both the maximiser and the minimiser have optimal pure stationary strategies. Firstly we form the matrix of undiscounted payoffs corresponding to each pair of pure stationary strategies (for each initial state) of the two players and prove that this matrix has a pure saddle point. Then by using the results by Derman [1] we prove the existence of optimal pure stationary strategy pair of the players. A crude but finite step algorithm is given to compute such an optimal pure stationary strategy pair of the players.