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...

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...

We present a complete picture of the relationship between the existence of 0-optimal strategies and ε-optimal strategies, ε>0, in the classes of stationary, Markov and history dependent strategies. Copyright Springer-Verlag Berlin Heidelberg 2002