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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The determinacy of infinite games with eventual perfect monitoring


Author: Eran Shmaya
Journal: Proc. Amer. Math. Soc. 139 (2011), 3665-3678
MSC (2010): Primary 91A15, 03E75; Secondary 03E15, 91A60
Published electronically: May 24, 2011
MathSciNet review: 2813396
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Abstract: An infinite two-player zero-sum game with a Borel winning set, in which the opponent's actions are monitored eventually but not necessarily immediately after they are played, is determined. The proof relies on a representation of the game as a stochastic game with perfect information, in which Chance operates as a delegate for the players and performs the randomizations for them, and on Martin's Theorem about the determinacy of such games.


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Additional Information

Eran Shmaya
Affiliation: Kellogg School of Management, Northwestern University, Evanston, Illinois 60208
Email: e-shmaya@kellogg.northwestern.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10987-0
PII: S 0002-9939(2011)10987-0
Keywords: Infinite games, determinacy, stochastic games, imperfect monitoring
Received by editor(s): July 5, 2010
Published electronically: May 24, 2011
Additional Notes: I thank the anonymous referee for helpful suggestions and comments, and also thank Chris Chambers, Tzachi Gilboa, John Levy, Ehud Lehrer, Wojciech Olszewski, Phil Reny, Eilon Solan, Bill Sudderth and Rakesh Vohra.
Communicated by: Ken Ono
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.