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Optimal markov strategies

Author

Listed:
  • William D. Sudderth

    (University of Minnesota)

Abstract

For discrete Dubins–Savage gambling problems (Markov decision processes) with payoff equal to the limsup of the utilities of the sequence of successive states, the existence of an optimal strategy at every fortune implies the existence of an optimal Markov strategy at every fortune. If the state space is finite, the same is true when the payoff is the liminf.

Suggested Citation

  • William D. Sudderth, 2020. "Optimal markov strategies," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 43-54, June.
    • Handle: RePEc:spr:decfin:v:43:y:2020:i:1:d:10.1007_s10203-019-00235-0
    DOI: 10.1007/s10203-019-00235-0
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    References listed on IDEAS

    as
    1. William D. Sudderth, 1983. "Gambling Problems with a Limit Inferior Payoff," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 287-297, May.
    2. William D. Sudderth, 2016. "Finitely Additive Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 92-108, February.
    3. Hill, Theodore P. & Pestien, Victor C., 1987. "The existence of good Markov strategies for decision processes with general payoffs," Stochastic Processes and their Applications, Elsevier, vol. 24(1), pages 61-76, February.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Gianluca Cassese & Pietro Rigo & Barbara Vantaggi, 2020. "A special issue on the mathematics of subjective probability," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 1-2, June.
    2. Pierpaolo Angelini & Fabrizio Maturo, 2020. "Non-Parametric Probability Distributions Embedded Inside of a Linear Space Provided with a Quadratic Metric," Mathematics, MDPI, vol. 8(11), pages 1-17, October.

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    More about this item

    Keywords

    Gambling theory; Markov decision processes; Optimal strategy; Stationary strategy; Markov strategy;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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