Discounted robust stochastic games with applications to homeland security and flow control

Restricted until 26 June 2009. This dissertation presents a distribution-free, robust optimization model for n-person finite state/action discounted stochastic games with incomplete information. We consider n-player, non-zero sum discounted stochastic games in which none of the players knows the true data of the game and each player considers a distribution-free incomplete information stochastic game to be played using robust optimization. We call such games discounted robust stochastic games. Discounted robust stochastic games allow us to use simple uncertainty sets for the unknown data of the game, and to eliminate the former approaches' requirements on defining prior probability distributions over a set of games. We prove the existence of equilibrium points when the payoffs of the game belong to a bounded set and the transition data is ambiguious. Unlike the prior work on incomplete information stochastic games, our approach lends itself to an explicit mathematical programming formulation for an equilibrium calculation. We illustrate the use of discounted robust stochastic games in a security related decision problem, followed by a control problem in a single server queuing system.