Zero and Non-zero Sum Risk-sensitive Semi-Markov Games

TL;DR

This paper investigates risk-sensitive semi-Markov games with finite states, proving the existence of game values and equilibrium strategies for both zero-sum and non-zero-sum scenarios.

Contribution

It establishes the existence of stationary saddle point and Nash equilibria in risk-sensitive semi-Markov games, extending game theory results to this setting.

Findings

Existence of game value in zero-sum case

Existence of stationary saddle point equilibrium

Existence of stationary Nash equilibrium in non-zero sum case

Abstract

In this article we consider zero and non-zero sum risk-sensitive average criterion games for semi-Markov processes with a finite state space. For the zero-sum case, under suitable assumptions we show that the game has a value. We also establish the existence of a stationary saddle point equilibrium. For the non-zero sum case, under suitable assumptions we establish the existence of a stationary Nash equilibrium.