Closed-Form Solutions To A Subclass Of Continuous Stochastic Games Via Symbolic Dynamic Programming

Zero-sum stochastic games provide a formalism to study competitive sequential interactions between two agents with diametrically opposing goals and evolving state. A solution to such games with discrete state was presented by Littman (Littman, 1994). The continuous state version of this game remains unsolved. In many instances continuous state solutions require non-linear optimisation, a problem for which closedform solutions are generally unavailable. We present an exact closed-form solution to a subclass of zero-sum continuous stochastic games that can be solved as a parameterised linear program by utilising symbolic dynamic programming. This novel technique is applied to calculate exact solutions to a variety of zero-sum continuous state stochastic games.