On Zero-Sum Two Person Perfect Information Semi-Markov Games

TL;DR

This paper proves that zero-sum two-person perfect information semi-Markov games have a well-defined value and optimal strategies, using saddle point analysis of payoff matrices.

Contribution

It establishes the existence of a game value and pure semi-stationary optimal strategies in PISMGs under the limiting ratio average payoff.

Findings

Existence of a game value in PISMGs.

Optimal pure semi-stationary strategies for both players.

Saddle point property of the payoff matrix.

Abstract

A zero-sum two-person Perfect Information Semi-Markov game (PISMG) under limiting ratio average payoff has a value and both the maximiser and the minimiser have optimal pure semi-stationary strategies. We arrive at the result by first fixing an arbitrary initial state and forming the matrix of undiscounted payoffs corresponding to each pair of pure stationary strategies of the two players and proving that this matrix has a pure saddle point.