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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On the existence of good Markov strategies
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by Theodore Preston Hill PDF
Trans. Amer. Math. Soc. 247 (1979), 157-176 Request permission

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
  • © Copyright 1979 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 247 (1979), 157-176
  • MSC: Primary 60G40
  • DOI: https://doi.org/10.1090/S0002-9947-1979-0517690-9
  • MathSciNet review: 517690