IDEAS home Printed from https://ideas.repec.org/a/pal/jorsoc/v59y2008i12d10.1057_palgrave.jors.2602518.html
   My bibliography  Save this article

A game-theoretic model for repeated assignment problem between two selfish agents

Author

Listed:
  • C G Lennon

    (Naval Postgraduate School, Monterey)

  • J M McGowan

    (Naval Postgraduate School, Monterey)

  • K Y Lin

    (Naval Postgraduate School, Monterey)

Abstract

This paper addresses a distributed system where a manager needs to assign a piece of equipment repeatedly between two selfish agents. On each day, each agent may encounter a task—routine or valuable—and can request the use of the manager's equipment to perform the task. Because the equipment benefits a valuable task more than a routine task, the manager wants to assign the equipment to a valuable task whenever possible. The two selfish agents, however, are only concerned with their own reward and do not have incentive to report their task types truthfully. To improve the system's overall performance, we design a token system such that an agent needs to spend tokens from his token bank to bid for the equipment. The two selfish agents become two players in a two-person non-zero-sum game. We find the Nash equilibrium of this game, and use numerical examples to illustrate the benefit of the token system.

Suggested Citation

  • C G Lennon & J M McGowan & K Y Lin, 2008. "A game-theoretic model for repeated assignment problem between two selfish agents," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(12), pages 1652-1658, December.
    • Handle: RePEc:pal:jorsoc:v:59:y:2008:i:12:d:10.1057_palgrave.jors.2602518
    DOI: 10.1057/palgrave.jors.2602518
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1057/palgrave.jors.2602518
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1057/palgrave.jors.2602518?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Cyrus Derman & Gerald J. Lieberman & Sheldon M. Ross, 1972. "A Sequential Stochastic Assignment Problem," Management Science, INFORMS, vol. 18(7), pages 349-355, March.
    2. Natividad Llorca & Stef Tijs & Judith Timmer, 2003. "Semi-infinite assignment problems and related games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(1), pages 67-78, April.
    3. Chris Albright & Cyrus Derman, 1972. "Asymptotic Optimal Policies for the Stochastic Sequential Assignment Problem," Management Science, INFORMS, vol. 19(1), pages 46-51, September.
    4. Rhonda Righter, 1989. "A Resource Allocation Problem in a Random Environment," Operations Research, INFORMS, vol. 37(2), pages 329-338, April.
    5. S. Christian Albright, 1974. "Optimal Sequential Assignments with Random Arrival Times," Management Science, INFORMS, vol. 21(1), pages 60-67, September.
    6. Llorca, N. & Tijs, S.H. & Timmer, J.B., 2003. "Semi-infinite assignment problems and related games," Other publications TiSEM 9fbdd989-c7af-49ab-87f2-8, Tilburg University, School of Economics and Management.
    7. Ehlers, Lars, 2002. "Coalitional Strategy-Proof House Allocation," Journal of Economic Theory, Elsevier, vol. 105(2), pages 298-317, August.
    8. D. P. Kennedy, 1986. "Optimal Sequential Assignment," Mathematics of Operations Research, INFORMS, vol. 11(4), pages 619-626, November.
    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. Xuanming Su & Stefanos A. Zenios, 2005. "Patient Choice in Kidney Allocation: A Sequential Stochastic Assignment Model," Operations Research, INFORMS, vol. 53(3), pages 443-455, June.
    2. Arash Khatibi & Sheldon H. Jacobson, 2016. "Doubly Stochastic Sequential Assignment Problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(2), pages 124-137, March.
    3. Tianke Feng & Joseph C. Hartman, 2015. "The dynamic and stochastic knapsack Problem with homogeneous‐sized items and postponement options," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(4), pages 267-292, June.
    4. David T. Wu & Sheldon M. Ross, 2015. "A stochastic assignment problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(1), pages 23-31, February.
    5. Meghan Shanks & Ge Yu & Sheldon H. Jacobson, 2023. "Approximation algorithms for stochastic online matching with reusable resources," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 98(1), pages 43-56, August.
    6. Alexander G. Nikolaev & Sheldon H. Jacobson, 2010. "Technical Note ---Stochastic Sequential Decision-Making with a Random Number of Jobs," Operations Research, INFORMS, vol. 58(4-part-1), pages 1023-1027, August.
    7. Baris Ata & Yichuan Ding & Stefanos Zenios, 2021. "An Achievable-Region-Based Approach for Kidney Allocation Policy Design with Endogenous Patient Choice," Manufacturing & Service Operations Management, INFORMS, vol. 23(1), pages 36-54, 1-2.
    8. Hak Chun, Young, 1996. "Selecting the best choice in the weighted secretary problem," European Journal of Operational Research, Elsevier, vol. 92(1), pages 135-147, July.
    9. Sheldon Ross & David Wu, 2013. "A generalized coupon collecting model as a parsimonious optimal stochastic assignment model," Annals of Operations Research, Springer, vol. 208(1), pages 133-146, September.
    10. Anton J. Kleywegt & Jason D. Papastavrou, 1998. "The Dynamic and Stochastic Knapsack Problem," Operations Research, INFORMS, vol. 46(1), pages 17-35, February.
    11. David, Israel & Levi, Ofer, 2001. "Asset-selling problems with holding costs," International Journal of Production Economics, Elsevier, vol. 71(1-3), pages 317-321, May.
    12. Sheldon M. Ross & Gideon Weiss & Zhengyu Zhang, 2021. "Technical Note—A Stochastic Assignment Problem with Unknown Eligibility Probabilities," Operations Research, INFORMS, vol. 69(1), pages 266-272, January.
    13. David, Israel & Levi, Ofer, 2004. "A new algorithm for the multi-item exponentially discounted optimal selection problem," European Journal of Operational Research, Elsevier, vol. 153(3), pages 782-789, March.
    14. Adrian Lee & Sheldon Jacobson, 2011. "Sequential stochastic assignment under uncertainty: estimation and convergence," Statistical Inference for Stochastic Processes, Springer, vol. 14(1), pages 21-46, February.
    15. Xuhan Tian & Junmin (Jim) Shi & Xiangtong Qi, 2022. "Stochastic Sequential Allocations for Creative Crowdsourcing," Production and Operations Management, Production and Operations Management Society, vol. 31(2), pages 697-714, February.
    16. Yizhaq Minchuk & Aner Sela, 2018. "Asymmetric sequential search under incomplete information," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 27(2), pages 315-325, June.
    17. Járai, Antal A., 2022. "Asymptotics of the optimum in discrete sequential assignment," Stochastic Processes and their Applications, Elsevier, vol. 148(C), pages 267-277.
    18. Francis Bloch & Nicolas Houy, 2012. "Optimal assignment of durable objects to successive agents," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(1), pages 13-33, September.
    19. R. Branzei & E. Gutiérrez & N. Llorca & J. Sánchez-Soriano, 2021. "Does it make sense to analyse a two-sided market as a multi-choice game?," Annals of Operations Research, Springer, vol. 301(1), pages 17-40, June.
    20. Arash Khatibi & Golshid Baharian & Banafsheh Behzad & Sheldon Jacobson, 2015. "Extensions of the sequential stochastic assignment problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(3), pages 317-340, December.

    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:pal:jorsoc:v:59:y:2008:i:12:d:10.1057_palgrave.jors.2602518. 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.palgrave-journals.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.