Saddle-point calculation for constrained finite Markov chains

This paper considers a zero-sum constrained stochastic game. The control objective of each participant is to optimize his limiting average payoff. In this case, the behavior of each player is modelled with a finite ergodic controlled Markov chain. The saddle point is shown to be the stationary strategy representing the solutions of two related Linear Programming Problems given in duality form. Several numerical examples illustrate the effectiveness of this suggested approach. In one of them, a single product market model is presented explaining the behavior of the game in a real situation. (C) 2002 Elsevier Science B.V. All rights reserved.