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A counterexample on overtaking optimality

Author

Listed:
  • Andrzej S. Nowak
  • Oscar Vega-Amaya

Abstract

Brown [3] constructed an aperiodic Markov decision chain in which no overtaking policy (stationary or nonstationary) exists. However, in his example a strong overtaking optimal policy exists in the class of all stationary policies. We provide another example of an aperiodic and geometric ergodic Markov decision chain which shows that the existence of a strong overtaking optimal stationary policy may fail inclusively in the class of stationary policies. We also give a brief survey of the existing literature on overtaking optimality in Markov decision chains. Copyright Springer-Verlag Berlin Heidelberg 1999

Suggested Citation

  • Andrzej S. Nowak & Oscar Vega-Amaya, 1999. "A counterexample on overtaking optimality," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(3), pages 435-439, July.
    • Handle: RePEc:spr:mathme:v:49:y:1999:i:3:p:435-439
    DOI: 10.1007/s001860050059
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    Cited by:

    1. Nowak, Andrzej S., 2008. "Equilibrium in a dynamic game of capital accumulation with the overtaking criterion," Economics Letters, Elsevier, vol. 99(2), pages 233-237, May.
    2. János Flesch & Arkadi Predtetchinski & Eilon Solan, 2017. "Sporadic Overtaking Optimality in Markov Decision Problems," Dynamic Games and Applications, Springer, vol. 7(2), pages 212-228, June.
    3. Galit Ashkenazi-Golan & János Flesch & Arkadi Predtetchinski & Eilon Solan, 2020. "Reachability and Safety Objectives in Markov Decision Processes on Long but Finite Horizons," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 945-965, June.
    4. Adam Jonsson, 2023. "An axiomatic approach to Markov decision processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(1), pages 117-133, February.

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