Computation of Suboptimal Nash Strategies for a Stochastic Differential Game under Partial Observation

摘要

Consider the random motion of two points in an open and bounded domain in the plane. Each of the velocities is perturbed by a corresponding Gaussian white noise. Two cases are dealt with: (1) each of the points can observe only its own location; (2) one can observe only its own location, but the other can observe the location of both points. The problem dealt with here is to find a strategy such that, in the sense of a Nash equilibrium point, the probabilities will both be maximized on a given class of (u,v)-admissible strategies. Sufficient conditions on weak optimal Nash equilibrium point strategies are derived, and weak suboptimal strategies computed for a variety of cases.