Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The completely mixed single-controller stochastic game


Author: Jerzy A. Filar
Journal: Proc. Amer. Math. Soc. 95 (1985), 585-594
MSC: Primary 90D15
MathSciNet review: 810169
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider a zero-sum stochastic game with finitely many states and actions. Further we assume that the transition probabilities depend on the actions of only one player (player II, in our case), and that the game is completely mixed. That is, every optimal stationary strategy for either player assigns a positive probability to every action in every state. For these games, properties analogous to those derived by Kaplansky [4] for the completely mixed matrix games, are established in this paper. These properties lead to the counterintuitive conclusion that the controller need not know the law of motion in order to play optimally, but his opponent does not have this luxury.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 90D15

Retrieve articles in all journals with MSC: 90D15


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0810169-4
PII: S 0002-9939(1985)0810169-4
Keywords: Stochastic games, single-controller, completely mixed property, stationary strategies
Article copyright: © Copyright 1985 American Mathematical Society