A Zero-Sum Stochastic Game with Compact Action Sets and no Asymptotic Value

Abstract

We give an example of a zero-sum stochastic game with four states, compact action sets for each player, and continuous payoff and transition functions, such that the discounted value does not converge as the discount factor tends to 0, and the value of the n-stage game does not converge as n goes to infinity. © 2013 Springer Science+Business Media New York.