Discounted Robust Stochastic Games and an Application to Queueing Control

This paper presents a robust optimization model for n-person finite state/action stochastic games with incomplete information. We consider nonzero sum discounted stochastic games in which none of the players knows the true data of a game, and each player adopts a robust optimization approach to address the uncertainty. We call these games discounted robust stochastic games. Such games allow us to use simple uncertainty sets for the unknown data and eliminate the need to have an a-priori probability distribution over a set of games. We prove the existence of equilibrium points and propose an explicit mathematical programming formulation for an equilibrium calculation. We illustrate the use of discounted robust stochastic games in a single server queueing control problem.