Semi-stationary Equilibrium Strategies in Non-cooperative N-person Semi-Markov Games

Abstract

AbstractFor a limiting ratio average (undiscounted) non-cooperative N-person semi-Markov game with finite state and action spaces, we prove that the solutions in the game where all players are restricted to semi-stationary strategies (that depend only on the initial state and the current state) are solutions for the unrestricted game. Furthermore, we consider zero-sum two-person semi-Markov games with action independent transitions (where the transition probabilities are independent of the actions of the players in each state) and prove the existence of an optimal semi-stationary strategy for each player. An example is provided to show that the semi-stationary optimal strategies cannot be strengthened further for such class of games.KeywordsSemi-Markov gamesLimiting ratio average payoffNash equilibriumAction independent transitionsOptimal semi-stationary strategiesMathemetics Subject Classification (2000)Primary: 91A15Secondary: 60G99