Guaranteed performance regions for Markov models

The objective is to extend D. Blackwell´s (1956) results to average payoff stochastic games. In stochastic games, the game matrix which is played at each stage depends on some state variable, which may change stochastically from stage to stage. The players´ choices at each stage control not only the payoffs, but also the game to be played at the next stage. Irreducible stochastic games are considered, in which the state process forms an irreducible Markov chain for any pair of stationary strategies. For a Markovian model of the system, the authors give a sufficient condition for approachability, and construct appropriate policies. The mathematical formulation leads to an approachability theory for stochastic games