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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Infinite games with imperfect information


Author: Michael Orkin
Journal: Trans. Amer. Math. Soc. 171 (1972), 501-507
MSC: Primary 90D05
MathSciNet review: 0312916
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Abstract: We consider an infinite, two person zero sum game played as follows: On the $ n$th move, players $ A,B$ select privately from fixed finite sets, $ {A_n},{B_n}$, the result of their selections being made known before the next selection is made. After an infinite number of selections, a point in the associated sequence space, $ \Omega $, is produced upon which $ B$ pays $ A$ an amount determined by a payoff function defined on $ \Omega $. In this paper we extend a result of Blackwell and show that if the payoff function is the indicator function of a set in the Boolean algebra generated by the $ {G_\delta }$'s (with respect to a natural topology on $ \Omega $) then the game in question has a value.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0312916-2
PII: S 0002-9947(1972)0312916-2
Keywords: Infinite games, imperfect information, two person zero sum game, lower value, payoff function, Baire function
Article copyright: © Copyright 1972 American Mathematical Society