IDEAS home Printed from https://ideas.repec.org/a/gam/jgames/v15y2024i3p17-d1397829.html
   My bibliography  Save this article

Invariant Equilibrium in Discontinuous Bayesian Games

Author

Listed:
  • Blake A. Allison

    (Department of Economics, Emory University, Atlanta, GA 30322, USA)

  • Jason J. Lepore

    (Department of Economics, Orfalea College of Business, California Polytechnic State University, San Luis Obispo, CA 93407, USA)

Abstract

We provide sufficient conditions on the primitives of a class of discontinuous Bayesian games such that all games in the class share equilibria. If a Bayesian game in the class also satisfies a weak efficiency condition, then we show its normal form is better-reply secure. The invariance property then provides an existence result for all Bayesian games in the class. Results are shown for both pure strategy and behavioral strategy equilibrium. We illustrate the application of the results with an example of a class of contests with bid caps.

Suggested Citation

  • Blake A. Allison & Jason J. Lepore, 2024. "Invariant Equilibrium in Discontinuous Bayesian Games," Games, MDPI, vol. 15(3), pages 1-14, May.
    • Handle: RePEc:gam:jgames:v:15:y:2024:i:3:p:17-:d:1397829
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2073-4336/15/3/17/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2073-4336/15/3/17/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Prokopovych, Pavlo & Yannelis, Nicholas C., 2014. "On the existence of mixed strategy Nash equilibria," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 87-97.
    2. Oriol Carbonell-Nicolau & Richard P. McLean, 2018. "On the Existence of Nash Equilibrium in Bayesian Games," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 100-129, February.
    3. Ezra Einy & Mridu Prabal Goswami & Ori Haimanko & Ram Orzach & Aner Sela, 2017. "Common-value all-pay auctions with asymmetric information," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(1), pages 79-102, March.
    4. Parreiras, Sérgio O. & Rubinchik, Anna, 2010. "Contests with three or more heterogeneous agents," Games and Economic Behavior, Elsevier, vol. 68(2), pages 703-715, March.
    5. Ron Siegel, 2010. "Asymmetric Contests with Conditional Investments," American Economic Review, American Economic Association, vol. 100(5), pages 2230-2260, December.
    6. Paul R. Milgrom & Robert J. Weber, 1985. "Distributional Strategies for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 619-632, November.
    7. Chen, Bo, 2019. "On the effects of bid caps in all-pay auctions," Economics Letters, Elsevier, vol. 177(C), pages 60-65.
    8. Amann, Erwin & Leininger, Wolfgang, 1996. "Asymmetric All-Pay Auctions with Incomplete Information: The Two-Player Case," Games and Economic Behavior, Elsevier, vol. 14(1), pages 1-18, May.
    9. He, Wei & Yannelis, Nicholas C., 2016. "Existence of equilibria in discontinuous Bayesian games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 181-194.
    10. Siegel, Ron, 2014. "Asymmetric all-pay auctions with interdependent valuations," Journal of Economic Theory, Elsevier, vol. 153(C), pages 684-702.
    11. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    12. Lizzeri, Alessandro & Persico, Nicola, 2000. "Uniqueness and Existence of Equilibrium in Auctions with a Reserve Price," Games and Economic Behavior, Elsevier, vol. 30(1), pages 83-114, January.
    13. Rentschler, Lucas & Turocy, Theodore L., 2016. "Two-bidder all-pay auctions with interdependent valuations, including the highly competitive case," Journal of Economic Theory, Elsevier, vol. 163(C), pages 435-466.
    14. Allison, Blake A. & Bagh, Adib & Lepore, Jason J., 2018. "Sufficient conditions for weak reciprocal upper semi-continuity in mixed extensions of games," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 99-107.
    15. Allison, Blake A. & Lepore, Jason J., 2014. "Verifying payoff security in the mixed extension of discontinuous games," Journal of Economic Theory, Elsevier, vol. 152(C), pages 291-303.
    16. Erik J. Balder, 1988. "Generalized Equilibrium Results for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 265-276, May.
    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. Prokopovych, Pavlo & Yannelis, Nicholas C., 2023. "On monotone pure-strategy Bayesian-Nash equilibria of a generalized contest," Games and Economic Behavior, Elsevier, vol. 140(C), pages 348-362.
    2. Oriol Carbonell-Nicolau & Richard P. McLean, 2018. "On the Existence of Nash Equilibrium in Bayesian Games," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 100-129, February.
    3. Fu, Qiang & Wu, Zenan & Zhu, Yuxuan, 2022. "On equilibrium existence in generalized multi-prize nested lottery contests," Journal of Economic Theory, Elsevier, vol. 200(C).
    4. Oriol Carbonell-Nicolau, 2021. "Equilibria in infinite games of incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 311-360, June.
    5. He, Wei & Yannelis, Nicholas C., 2016. "Existence of equilibria in discontinuous Bayesian games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 181-194.
    6. Prokopovych, Pavlo & Yannelis, Nicholas C., 2019. "On monotone approximate and exact equilibria of an asymmetric first-price auction with affiliated private information," Journal of Economic Theory, Elsevier, vol. 184(C).
    7. Allison, Blake A. & Bagh, Adib & Lepore, Jason J., 2022. "Invariant equilibria and classes of equivalent games," Games and Economic Behavior, Elsevier, vol. 132(C), pages 448-462.
    8. Oriol Carbonell-Nicolau & Richard P. McLean, 2019. "Nash and Bayes–Nash equilibria in strategic-form games with intransitivities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(4), pages 935-965, November.
    9. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.
    10. Olszewski, Wojciech & Siegel, Ron, 2023. "Equilibrium existence in games with ties," Theoretical Economics, Econometric Society, vol. 18(2), May.
    11. Lu, Jingfeng & Parreiras, Sérgio O., 2017. "Monotone equilibrium of two-bidder all-pay auctions Redux," Games and Economic Behavior, Elsevier, vol. 104(C), pages 78-91.
    12. Rentschler, Lucas & Turocy, Theodore L., 2016. "Two-bidder all-pay auctions with interdependent valuations, including the highly competitive case," Journal of Economic Theory, Elsevier, vol. 163(C), pages 435-466.
    13. Xiao, Jun, 2018. "Equilibrium analysis of the all-pay contest with two nonidentical prizes: Complete results," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 21-34.
    14. Zheng, Charles Z., 2019. "Necessary and sufficient conditions for peace: Implementability versus security," Journal of Economic Theory, Elsevier, vol. 180(C), pages 135-166.
    15. Ori Haimanko, 2021. "Bayesian Nash equilibrium existence in (almost continuous) contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 1231-1258, April.
    16. Jingfeng Lu & Hongkun Ma & Zhe Wang, 2018. "Ranking Disclosure Policies In All‐Pay Auctions," Economic Inquiry, Western Economic Association International, vol. 56(3), pages 1464-1485, July.
    17. Zhuoqiong Chen, 2021. "All-pay auctions with private signals about opponents’ values," Review of Economic Design, Springer;Society for Economic Design, vol. 25(1), pages 33-64, June.
    18. Oriol Carbonell-Nicolau, 2021. "Perfect equilibria in games of incomplete information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(4), pages 1591-1648, June.
    19. Xiao, Jun, 2016. "Asymmetric all-pay contests with heterogeneous prizes," Journal of Economic Theory, Elsevier, vol. 163(C), pages 178-221.
    20. Wei He & Xiang Sun & Yeneng Sun & Yishu Zeng, 2021. "Characterization of equilibrium existence and purification in general Bayesian games," Papers 2106.08563, arXiv.org.

    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:gam:jgames:v:15:y:2024:i:3:p:17-:d:1397829. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.