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Computation of suboptimal Nash strategies for a stochastic differential game under partial observation†

1982; Taylor & Francis; Volume: 13; Issue: 10 Linguagem: Inglês

10.1080/00207728208926413

1464-5319

Y. Yavin,

Game Theory and Voting Systems

Consider the random motion of two points Me and Mp in an open and bounded domain Δ0 in the plane. Each of the velocities, u = (u1, u2) of Me and v = (v1,v2) of Mp , is perturbed by a corresponding ℝ2-valued gaussian white noise. Two cases are dealt with : (A) Each of the points can observe only its own location ; (B) Me can observe only its own location, but Mp can observe the location of both points. Let Δ T and Δ f be two disjoint closed subsets of Δ0. Denote by ℰ1 and ℰ2 the following events : ℰ1 = { Mp intercepts Me in Δ f before Me reaches tho set ΔT and before either Me or Mp has left Δ0}, and ℰ2 = { Me reaches the set Δ T before being intercepted by Mp , and before either Mp or Me has left Δ0}. The problem dealt with hero is to find a strategy (u∗, v∗) such that, in the sense of a Nash equilibrium point, the probabilities Prob (ℰ1) and Prob (ℰ2) will both be maximized on a given class of (u,v)- inadmissible strategies. Sufficient conditions on weak optimal Nash equilibrium point strategies are derived, and weak suboptimal strategies computed for a variety of cases.