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

 

On the existence of good Markov strategies


Author: Theodore Preston Hill
Journal: Trans. Amer. Math. Soc. 247 (1979), 157-176
MSC: Primary 60G40
MathSciNet review: 517690
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Abstract: In contrast to the known fact that there are gambling problems based on a finite state space for which no stationary family of strategies is at all good, in every such problem there always exist $ \varepsilon $-optimal Markov families (in which the strategy depends only on the current state and time) and also $ \varepsilon $-optimal tracking families (in which the strategy depends only on the current state and the number of times that state has been previously visited). More generally, this result holds for all finite state gambling problems with a payoff which is shift and permutation invariant.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1979-0517690-9
PII: S 0002-9947(1979)0517690-9
Keywords: Markov chain, gambling theory, strategy, stationary strategy, Markov strategy, stochastic process, dynamic programming, optimization, decision theory, control theory
Article copyright: © Copyright 1979 American Mathematical Society