IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v21y1975i9p967-975.html
   My bibliography  Save this article

Ordinal Dynamic Programming

Author

Listed:
  • Matthew J. Sobel

    (Yale University)

Abstract

Numerically valued reward processes are found in most dynamic programming models. Mitten, however, recently formulated finite horizon sequential decision processes in which a real-valued reward need not be earned at each stage. Instead of the cardinality assumption implicit in past models, Mitten assumes that a decision maker has a preference order over a general collection of outcomes (which need not be numerically valued). This paper investigates infinite horizon ordinal dynamic programming models. Both deterministic and stochastic models are considered. It is shown that an optimal policy exists if and only if some stationary policy is optimal. Moreover, "policy improvement" leads to better policies using either Howard-Blackwell or Eaton-Zadeh procedures. The results illuminate the roles played by various sets of assumptions in the literature on Markovian decision processes.

Suggested Citation

  • Matthew J. Sobel, 1975. "Ordinal Dynamic Programming," Management Science, INFORMS, vol. 21(9), pages 967-975, May.
    • Handle: RePEc:inm:ormnsc:v:21:y:1975:i:9:p:967-975
    DOI: 10.1287/mnsc.21.9.967
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.21.9.967
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.21.9.967?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Trzaskalik, Tadeusz & Sitarz, Sebastian, 2007. "Discrete dynamic programming with outcomes in random variable structures," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1535-1548, March.
    2. Matthew Sobel, 2013. "Discounting axioms imply risk neutrality," Annals of Operations Research, Springer, vol. 208(1), pages 417-432, September.
    3. Peter A. Streufert, 2023. "Dynamic Programming for Pure-Strategy Subgame Perfection in an Arbitrary Game," Papers 2302.03855, arXiv.org, revised Mar 2023.
    4. Hammond, Peter J & Zank, Horst, 2013. "Rationality and Dynamic Consistency under Risk and Uncertainty," The Warwick Economics Research Paper Series (TWERPS) 1033, University of Warwick, Department of Economics.
    5. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2017. "Does backwards induction imply subgame perfection?," Games and Economic Behavior, Elsevier, vol. 103(C), pages 19-29.
    6. Frini, Anissa & Guitouni, Adel & Martel, Jean-Marc, 2012. "A general decomposition approach for multi-criteria decision trees," European Journal of Operational Research, Elsevier, vol. 220(2), pages 452-460.
    7. Maciej Nowak & Tadeusz Trzaskalik, 2013. "Interactive procedure for a multiobjective stochastic discrete dynamic problem," Journal of Global Optimization, Springer, vol. 57(2), pages 315-330, October.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:21:y:1975:i:9:p:967-975. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.