Random fixed points of multifunctions in games and dynamic programming



Abstract

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.


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Published : 1986-09-30


NowakA. (1986). Random fixed points of multifunctions in games and dynamic programming. Annales Mathematicae Silesianae, 2, 53-59. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14321

Andrzej Nowak 
Instytut Matematyki, Uniwersytet Śląski w Katowicach  Poland



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