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 nonlinear 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.