Random fixed points of multifunctions in games and dynamic programming
Andrzej S. Nowak · PUBLISHING HOUSE OF THE UNIVERSITY OF SILESIA (University of Silesia) · 1986
Recently several authors demonstrated random fixed point theorems for various classes of multifunctions ([7], [8], [2], [3], [12], [10]). On the other hand we do not know any work on applications of these theorems. In this paper we apply to games and dynamic programming a random analogue of the Fan-Kakutani fixed point theorem. We consider a zero-sum two-person game depending on a random parameter, and present sufficient conditions for the existence of a measurable solution. Then we study the existence of measurable stationary optimal programs in discounted dynamic programming with a random parameter.