IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v65y2018i8p580-593.html
   My bibliography  Save this article

Finite‐horizon Markov population decision chains with constant risk posture

Author

Listed:
  • Amanda M. White
  • Pelin G. Canbolat

Abstract

A Markov population decision chain concerns the control of a population of individuals in different states by assigning an action to each individual in the system in each period. This article solves the problem of finding policies that maximize expected system utility over a finite horizon in Markov population decision chains with finite state‐action space under the following assumptions: (1) The utility function exhibits constant risk posture, (2) the progeny vectors of distinct individuals are independent, and (3) the progeny vectors of individuals in a state who take the same action are identically distributed. The main result is that it is possible to solve the problem with the original state‐action space without augmenting it to include information about the population in each state or any other aspect of the system history. In particular, there exists an optimal policy that assigns the same action to all individuals in a given state and period, independently of the population in that period and such a policy can be computed efficiently. The optimal utility operators that find the maximum of a finite collection of polynomials (rather than affine functions) yield an optimal solution with effort linear in the number of periods. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 65: 580–593, 2018

Suggested Citation

  • Amanda M. White & Pelin G. Canbolat, 2018. "Finite‐horizon Markov population decision chains with constant risk posture," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(8), pages 580-593, December.
    • Handle: RePEc:wly:navres:v:65:y:2018:i:8:p:580-593
    DOI: 10.1002/nav.21698
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.21698
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.21698?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
    ---><---

    References listed on IDEAS

    as
    1. David M. Kreps, 1977. "Decision Problems with Expected Utility Criteria, II: Stationarity," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 266-274, August.
    2. Pelin Canbolat, 2014. "Optimal halting policies in Markov population decision chains with constant risk posture," Annals of Operations Research, Springer, vol. 222(1), pages 227-237, November.
    3. Melike Baykal-Gürsoy & Keith W. Ross, 1992. "Variability Sensitive Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 17(3), pages 558-571, August.
    4. David M. Kreps, 1977. "Decision Problems with Expected Utility Critera, I: Upper and Lower Convergent Utility," Mathematics of Operations Research, INFORMS, vol. 2(1), pages 45-53, February.
    5. Rothblum, Uriel G., 1975. "Multivariate constant risk posture," Journal of Economic Theory, Elsevier, vol. 10(3), pages 309-332, June.
    6. Uriel G. Rothblum, 1984. "Multiplicative Markov Decision Chains," Mathematics of Operations Research, INFORMS, vol. 9(1), pages 6-24, February.
    7. Matthew Sobel, 2013. "Discounting axioms imply risk neutrality," Annals of Operations Research, Springer, vol. 208(1), pages 417-432, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pelin Canbolat, 2014. "Optimal halting policies in Markov population decision chains with constant risk posture," Annals of Operations Research, Springer, vol. 222(1), pages 227-237, November.
    2. Peter A. Streufert, 2023. "Dynamic Programming for Pure-Strategy Subgame Perfection in an Arbitrary Game," Papers 2302.03855, arXiv.org, revised Mar 2023.
    3. Basu, Arnab & Ghosh, Mrinal Kanti, 2014. "Zero-sum risk-sensitive stochastic games on a countable state space," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 961-983.
    4. V. S. Borkar & S. P. Meyn, 2002. "Risk-Sensitive Optimal Control for Markov Decision Processes with Monotone Cost," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 192-209, February.
    5. Alessandro Arlotto & Noah Gans & J. Michael Steele, 2014. "Markov Decision Problems Where Means Bound Variances," Operations Research, INFORMS, vol. 62(4), pages 864-875, August.
    6. Rolando Cavazos-Cadena, 2018. "Characterization of the Optimal Risk-Sensitive Average Cost in Denumerable Markov Decision Chains," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 1025-1050, August.
    7. Mikhail Sokolov, 2011. "Interval scalability of rank-dependent utility," Theory and Decision, Springer, vol. 70(3), pages 255-282, March.
    8. Arie Leizarowitz, 2003. "An Algorithm to Identify and Compute Average Optimal Policies in Multichain Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 553-586, August.
    9. 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.
    10. Dilip Abreu & David Pearce & Ennio Stacchetti, 1997. "Optimal Cartel Equilibria with Imperfect monitoring," Levine's Working Paper Archive 632, David K. Levine.
    11. Lucy Gongtao Chen & Daniel Zhuoyu Long & Melvyn Sim, 2015. "On Dynamic Decision Making to Meet Consumption Targets," Operations Research, INFORMS, vol. 63(5), pages 1117-1130, October.
    12. Marc St-Pierre, 2017. "Risk-induced discounting," Theory and Decision, Springer, vol. 82(1), pages 13-30, January.
    13. HuiChen Chiang, 2007. "Financial intermediary's choice of borrowing," Applied Economics, Taylor & Francis Journals, vol. 40(2), pages 251-260.
    14. Kitti, Mitri, 2018. "Sustainable social choice under risk," Mathematical Social Sciences, Elsevier, vol. 94(C), pages 19-31.
    15. Pelin G. Canbolat & Uriel G. Rothblum, 2019. "Constant risk aversion in stochastic contests with exponential completion times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(1), pages 4-14, February.
    16. Alex Bloedel & R. Vijay Krishna & Oksana Leukhina, 2018. "Insurance and Inequality with Persistent Private Information," Working Papers 2018-020, Federal Reserve Bank of St. Louis, revised 11 Aug 2024.
    17. Peter H. Farquhar & Yutaka Nakamura, 1988. "Utility assessment procedures for polynomial‐exponential functions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(6), pages 597-613, December.
    18. Hui Chen Chiang, 2007. "Optimal prepayment behaviour," Applied Economics Letters, Taylor & Francis Journals, vol. 14(15), pages 1127-1129.
    19. Takayuki Osogami, 2012. "Iterated risk measures for risk-sensitive Markov decision processes with discounted cost," Papers 1202.3755, arXiv.org.
    20. Dilip Abreu & David G. Pearce & Ennio Stacchetti, 1986. "Toward a Theory of Discounted Repeated Games with Imperfect Monitoring," Cowles Foundation Discussion Papers 791, Cowles Foundation for Research in Economics, Yale University.

    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:wly:navres:v:65:y:2018:i:8:p:580-593. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.