IDEAS home Printed from https://ideas.repec.org/a/spr/joinma/v28y2017i3d10.1007_s10845-014-1010-8.html
   My bibliography  Save this article

Bayesian equilibria for uncertain bimatrix game with asymmetric information

Author

Listed:
  • Xiangfeng Yang

    (Renmin University of China
    Tsinghua University)

  • Jinwu Gao

    (Renmin University of China)

Abstract

In an uncertain bimatrix game, there are two solution concepts of $$(\alpha ,\beta )$$ ( α , β ) -optimistic equilibrium strategy and $$(u,v)$$ ( u , v ) -maximum chance equilibrium strategy. This paper goes further by assuming that the confidence levels $$\alpha , \beta $$ α , β and payoff levels $$u, v$$ u , v are private information. Then, the so-called uncertain bimatrix game with asymmetric information is investigated. Two solution concepts of Bayesian optimistic equilibrium strategy and Bayesian maximum chance equilibrium strategy as well as their existence theorems are presented. Moreover, sufficient and necessary conditions are given for finding the Bayesian equilibrium strategies. Finally, a two-firm advertising problem is analyzed for illustrating our modelling idea.

Suggested Citation

  • Xiangfeng Yang & Jinwu Gao, 2017. "Bayesian equilibria for uncertain bimatrix game with asymmetric information," Journal of Intelligent Manufacturing, Springer, vol. 28(3), pages 515-525, March.
    • Handle: RePEc:spr:joinma:v:28:y:2017:i:3:d:10.1007_s10845-014-1010-8
    DOI: 10.1007/s10845-014-1010-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10845-014-1010-8
    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/s10845-014-1010-8?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. Roger A. Blau, 1974. "Random-Payoff Two-Person Zero-Sum Games," Operations Research, INFORMS, vol. 22(6), pages 1243-1251, December.
    2. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
    3. R. G. Cassidy & C. A. Field & M. J. L. Kirby, 1972. "Solution of a Satisficing Model for Random Payoff Games," Management Science, INFORMS, vol. 19(3), pages 266-271, November.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Boyang Dai & Xiangfeng Yang & Xiaoyue Liu, 2022. "Shapley Value of Uncertain Coalitional Game based on Hurwicz Criterion with Application to Water Resource Allocation," Group Decision and Negotiation, Springer, vol. 31(1), pages 241-260, February.

    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. Singh, Vikas Vikram & Lisser, Abdel & Arora, Monika, 2021. "An equivalent mathematical program for games with random constraints," Statistics & Probability Letters, Elsevier, vol. 174(C).
    2. Chunsheng Cui & Zhongwei Feng & Chunqiao Tan, 2018. "Credibilistic Loss Aversion Nash Equilibrium for Bimatrix Games with Triangular Fuzzy Payoffs," Complexity, Hindawi, vol. 2018, pages 1-16, December.
    3. Rossana Riccardi & Giorgia Oggioni & Elisabetta Allevi & Abdel Lisser, 2023. "Complementarity formulation of games with random payoffs," Computational Management Science, Springer, vol. 20(1), pages 1-32, December.
    4. Singh, Vikas Vikram & Lisser, Abdel, 2019. "A second-order cone programming formulation for two player zero-sum games with chance constraints," European Journal of Operational Research, Elsevier, vol. 275(3), pages 839-845.
    5. Shen Peng & Navnit Yadav & Abdel Lisser & Vikas Vikram Singh, 2021. "Chance-constrained games with mixture distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(1), pages 71-97, August.
    6. Cheng, Jianqiang & Leung, Janny & Lisser, Abdel, 2016. "Random-payoff two-person zero-sum game with joint chance constraints," European Journal of Operational Research, Elsevier, vol. 252(1), pages 213-219.
    7. Maxime Menuet & Petros G. Sekeris, 2021. "Overconfidence and conflict," Economic Inquiry, Western Economic Association International, vol. 59(4), pages 1483-1499, October.
    8. Andrés Perea & Elias Tsakas, 2019. "Limited focus in dynamic games," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 571-607, June.
    9. Simai He & Jay Sethuraman & Xuan Wang & Jiawei Zhang, 2017. "A NonCooperative Approach to Cost Allocation in Joint Replenishment," Operations Research, INFORMS, vol. 65(6), pages 1562-1573, December.
    10. Bommer, Rolf, 1995. "Environmental policy and industrial competitiveness: The pollution haven hypothesis reconsidered," Discussion Papers, Series II 262, University of Konstanz, Collaborative Research Centre (SFB) 178 "Internationalization of the Economy".
    11. Martin Shubik, 1980. "Perfect or Robust Noncooperative Equilibrium: A Search for the Philosophers Stone?," Cowles Foundation Discussion Papers 559, Cowles Foundation for Research in Economics, Yale University.
    12. Martin Meier & Burkhard Schipper, 2014. "Bayesian games with unawareness and unawareness perfection," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 219-249, June.
    13. Ming Chen & Sareh Nabi & Marciano Siniscalchi, 2023. "Advancing Ad Auction Realism: Practical Insights & Modeling Implications," Papers 2307.11732, arXiv.org, revised Apr 2024.
    14. Giuseppe Attanasi & Pierpaolo Battigalli & Elena Manzoni, 2016. "Incomplete-Information Models of Guilt Aversion in the Trust Game," Management Science, INFORMS, vol. 62(3), pages 648-667, March.
    15. Huseyin Cavusoglu & Srinivasan Raghunathan, 2004. "Configuration of Detection Software: A Comparison of Decision and Game Theory Approaches," Decision Analysis, INFORMS, vol. 1(3), pages 131-148, September.
    16. Strzalecki, Tomasz, 2014. "Depth of reasoning and higher order beliefs," Journal of Economic Behavior & Organization, Elsevier, vol. 108(C), pages 108-122.
    17. Schaefer, Alexander, 2021. "Rationality, uncertainty, and unanimity: an epistemic critique of contractarianism," Economics and Philosophy, Cambridge University Press, vol. 37(1), pages 82-117, March.
    18. Kaufmann, Lutz & Roessing, Soenke, 2005. "Managing conflict of interests between headquarters and their subsidiaries regarding technology transfer to emerging markets--a framework," Journal of World Business, Elsevier, vol. 40(3), pages 235-253, August.
    19. Yoo, Seung Han, 2014. "Learning a population distribution," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 188-201.
    20. Giovanni Paolo Crespi & Davide Radi & Matteo Rocca, 2017. "Robust games: theory and application to a Cournot duopoly model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 177-198, November.

    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:joinma:v:28:y:2017:i:3:d:10.1007_s10845-014-1010-8. 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.