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Markov-achievable payoffs for finite-horizon decision models

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  • Pestien, Victor
  • Wang, Xiaobo

Abstract

Consider the class of n-stage decision models with state space S, action space A, and payoff function g : (S x A)n x S --> R. The function g is Markov-achievable if for any possible set of available randomized actions and all transition laws, each plan has a corresponding Markov plan whose value is at least as good. A condition on g, called the "non-forking linear sections property", is necessary and sufficient for g to be Markov achievable. If g satisfies the slightly stronger "general linear sections property", then g can be written as a sum of products of certain simple neighboring-stage payoffs.

Suggested Citation

  • Pestien, Victor & Wang, Xiaobo, 1998. "Markov-achievable payoffs for finite-horizon decision models," Stochastic Processes and their Applications, Elsevier, vol. 73(1), pages 101-118, January.
    • Handle: RePEc:eee:spapps:v:73:y:1998:i:1:p:101-118
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    References listed on IDEAS

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    1. Pestien, Victor & Wang, Xiaobo, 1993. "Finite-stage reward functions having the Markov adequacy property," Stochastic Processes and their Applications, Elsevier, vol. 46(1), pages 129-151, May.
    2. Uriel G. Rothblum, 1984. "Multiplicative Markov Decision Chains," Mathematics of Operations Research, INFORMS, vol. 9(1), pages 6-24, February.
    3. Eugene A. Feinberg & Adam Shwartz, 1995. "Constrained Markov Decision Models with Weighted Discounted Rewards," Mathematics of Operations Research, INFORMS, vol. 20(2), pages 302-320, May.
    4. 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.
    5. Ronald A. Howard & James E. Matheson, 1972. "Risk-Sensitive Markov Decision Processes," Management Science, INFORMS, vol. 18(7), pages 356-369, March.
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