IDEAS home Printed from https://ideas.repec.org/a/spr/dyngam/v14y2024i4d10.1007_s13235-023-00539-2.html
   My bibliography  Save this article

Competition and Recall in Selection Problems

Author

Listed:
  • Fabien Gensbittel

    (University of Toulouse Capitole)

  • Dana Pizarro

    (Universidad de O’Higgins)

  • Jérôme Renault

    (University of Toulouse Capitole)

Abstract

We extend the prophet inequality problem to a competitive setting. At every period, a new realization of a random variable with a known distribution arrives, which is publicly observed. Then, two players simultaneously decide whether to pick an available value or to pass and wait until the next period (ties are broken uniformly at random). As soon as a player gets a value, he leaves the market and his payoff is the value of this realization. In the first variant, namely the “no recall” case, the agents can only bid at each period for the current value. In a second variant, the “full recall” case, the agents can also bid for any of the previous realizations which has not been already selected. For each variant, we study the subgame-perfect Nash equilibrium payoffs of the corresponding game. More specifically, we give a full characterization in the full recall case and show in particular that the expected payoffs of the players at any equilibrium are always equal, whereas in the no recall case the set of equilibrium payoffs typically has full dimension. Regarding the welfare at equilibrium, surprisingly the best equilibrium payoff a player can have may be strictly higher in the no recall case. However, the sum of equilibrium payoffs is weakly larger when the players have full recall. Finally, we show that in the case of 2 arrivals and arbitrary distributions, the prices of Anarchy and Stability in the no recall case are at most 4/3, and this bound is tight.

Suggested Citation

  • Fabien Gensbittel & Dana Pizarro & Jérôme Renault, 2024. "Competition and Recall in Selection Problems," Dynamic Games and Applications, Springer, vol. 14(4), pages 806-845, September.
  • Handle: RePEc:spr:dyngam:v:14:y:2024:i:4:d:10.1007_s13235-023-00539-2
    DOI: 10.1007/s13235-023-00539-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13235-023-00539-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s13235-023-00539-2?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
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. D. V. Lindley, 1961. "Dynamic Programming and Decision Theory," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 10(1), pages 39-51, March.
    2. Kertz, Robert P., 1986. "Stop rule and supremum expectations of i.i.d. random variables: A complete comparison by conjugate duality," Journal of Multivariate Analysis, Elsevier, vol. 19(1), pages 88-112, June.
    3. Fouad Abdelaziz & Saoussen Krichen, 2007. "Optimal stopping problems by two or more decision makers: a survey," Computational Management Science, Springer, vol. 4(2), pages 89-111, April.
    4. Minoru Sakaguchi & Vladimir V. Mazalov, 2004. "A non-zero-sum no-information best-choice game," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(3), pages 437-451, December.
    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. Vincent Mak & Darryl A. Seale & Amnon Rapoport & Eyran J. Gisches, 2019. "Voting Rules in Sequential Search by Committees: Theory and Experiments," Management Science, INFORMS, vol. 65(9), pages 4349-4364, September.
    2. Mak, Vincent & Rapoport, Amnon & Seale, Darryl A., 2014. "Sequential search by groups with rank-dependent payoffs: An experimental study," Organizational Behavior and Human Decision Processes, Elsevier, vol. 124(2), pages 256-267.
    3. Fouad Ben Abdelaziz & Ray Saadaoui Mallek, 2018. "Multi-criteria optimal stopping methods applied to the portfolio optimisation problem," Annals of Operations Research, Springer, vol. 267(1), pages 29-46, August.
    4. Daniel Cownden & David Steinsaltz, 2014. "Effects of Competition in a Secretary Problem," Operations Research, INFORMS, vol. 62(1), pages 104-113, February.
    5. Rohan DUTTA, 2016. "Joint Search with No Information: An Inefficient Immediate Agreement Theorem," Cahiers de recherche 12-2016, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    6. Dutta, Rohan, 2017. "Joint search with no information: An immediate agreement theorem," Economics Letters, Elsevier, vol. 160(C), pages 43-45.
    7. Chun, Young H. & Plante, Robert D. & Schneider, Helmut, 2002. "Buying and selling an asset over the finite time horizon: A non-parametric approach," European Journal of Operational Research, Elsevier, vol. 136(1), pages 106-120, January.
    8. Ravi Jagannathan & Iwan Meier, 2002. "Do We Need CAPM for Capital Budgeting?," Financial Management, Financial Management Association, vol. 31(4), Winter.
    9. Saint-Mont, Uwe, 2002. "A Simple Derivation of a Complicated Prophet Region," Journal of Multivariate Analysis, Elsevier, vol. 80(1), pages 67-72, January.
    10. Kimmo Eriksson & Jonas Sjöstrand & Pontus Strimling, 2007. "Optimal Expected Rank in a Two-Sided Secretary Problem," Operations Research, INFORMS, vol. 55(5), pages 921-931, October.
    11. Schaffner, Florian, 2016. "Information transmission in high dimensional choice problems: The value of online ratings in the restaurant market," VfS Annual Conference 2016 (Augsburg): Demographic Change 145585, Verein für Socialpolitik / German Economic Association.
    12. L. Bayón & P. Fortuny Ayuso & J. M. Grau & A. M. Oller-Marcén & M. M. Ruiz, 2018. "The Best-or-Worst and the Postdoc problems," Journal of Combinatorial Optimization, Springer, vol. 35(3), pages 703-723, April.
    13. José A. Soto & Abner Turkieltaub & Victor Verdugo, 2021. "Strong Algorithms for the Ordinal Matroid Secretary Problem," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 642-673, May.
    14. Deutsch, Yael & David, Israel, 2021. "Promoting assets selling through advertisement channels," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    15. Stein, William E. & Seale, Darryl A. & Rapoport, Amnon, 2003. "Analysis of heuristic solutions to the best choice problem," European Journal of Operational Research, Elsevier, vol. 151(1), pages 140-152, November.
    16. Wojciech Kaźmierczak, 2016. "The best choice problem for posets; colored complete binary trees," Journal of Combinatorial Optimization, Springer, vol. 31(1), pages 13-28, January.
    17. Fouad Abdelaziz & Saoussen Krichen, 2007. "Optimal stopping problems by two or more decision makers: a survey," Computational Management Science, Springer, vol. 4(2), pages 89-111, April.
    18. Whitmeyer Mark, 2018. "A Competitive Optimal Stopping Game," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 18(1), pages 1-15, January.
    19. Yaakov Malinovsky & Gregory Haber & Paul S. Albert, 2020. "An optimal design for hierarchical generalized group testing," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(3), pages 607-621, June.
    20. Sadoghi, Amirhossein & Vecer, Jan, 2022. "Optimal liquidation problem in illiquid markets," European Journal of Operational Research, Elsevier, vol. 296(3), pages 1050-1066.

    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:spr:dyngam:v:14:y:2024:i:4:d:10.1007_s13235-023-00539-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.