IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v104y2023ics0304406822001306.html
   My bibliography  Save this article

Equilibrium existence in contests with bid caps

Author

Listed:
  • Olszewski, Wojciech
  • Siegel, Ron

Abstract

We prove equilibrium existence in distributional strategies for a general class of multiprize contests, including contests with bid caps. Contests with bid caps violate the assumptions of Reny’s (1999) equilibrium existence results as well as those of many other existence results. The equilibrium existence proof we provide for contests with bid caps refers to a special property of such contests, whereas the proof is much more straightforward for contests without a bid cap.

Suggested Citation

  • Olszewski, Wojciech & Siegel, Ron, 2023. "Equilibrium existence in contests with bid caps," Journal of Mathematical Economics, Elsevier, vol. 104(C).
  • Handle: RePEc:eee:mateco:v:104:y:2023:i:c:s0304406822001306
    DOI: 10.1016/j.jmateco.2022.102804
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406822001306
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jmateco.2022.102804?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. Szech, Nora, 2015. "Tie-breaks and bid-caps in all-pay auctions," Games and Economic Behavior, Elsevier, vol. 92(C), pages 138-149.
    2. Philip J. Reny, 2020. "Nash Equilibrium in Discontinuous Games," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 439-470, August.
    3. Arieh Gavious & Benny Moldovanu & Aner Sela, 2002. "Bid Costs and Endogenous Bid Caps," RAND Journal of Economics, The RAND Corporation, vol. 33(4), pages 709-722, Winter.
    4. Yeon-Koo Che & Ian L. Gale, 2008. "Caps on Political Lobbying," Springer Books, in: Roger D. Congleton & Kai A. Konrad & Arye L. Hillman (ed.), 40 Years of Research on Rent Seeking 2, pages 337-345, Springer.
    5. 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.
    6. Olszewski, Wojciech & Siegel, Ron, 2019. "Bid caps in large contests," Games and Economic Behavior, Elsevier, vol. 115(C), pages 101-112.
    7. He, Wei & Yannelis, Nicholas C., 2016. "Existence of equilibria in discontinuous Bayesian games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 181-194.
    8. Carmona, Guilherme & Podczeck, Konrad, 2018. "Invariance of the equilibrium set of games with an endogenous sharing rule," Journal of Economic Theory, Elsevier, vol. 177(C), pages 1-33.
    9. 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.
    10. Olszewski, Wojciech & Siegel, Ron, 2023. "Equilibrium existence in games with ties," Theoretical Economics, Econometric Society, vol. 18(2), May.
    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. Sela, Aner, 2023. "Two-stage elimination games," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    2. Levine, David K. & Mattozzi, Andrea & Modica, Salvatore, 2024. "The tripartite auction folk theorem," European Economic Review, Elsevier, vol. 162(C).

    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. Olszewski, Wojciech & Siegel, Ron, 2023. "Equilibrium existence in games with ties," Theoretical Economics, Econometric Society, vol. 18(2), May.
    2. Olszewski, Wojciech & Siegel, Ron, 2019. "Bid caps in large contests," Games and Economic Behavior, Elsevier, vol. 115(C), pages 101-112.
    3. Chen, Bo & Serena, Marco, 2023. "Disclosure Policies in All-Pay Auctions with Bid Caps," Journal of Economic Behavior & Organization, Elsevier, vol. 209(C), pages 141-160.
    4. 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.
    5. Chen, Bo & Ma, Lijun & Zhu, Zhaobo & Zhou, Yu, 2020. "Disclosure policies in all-pay auctions with bid caps and stochastic entry," Economics Letters, Elsevier, vol. 186(C).
    6. 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).
    7. Wei He & Xiang Sun & Yeneng Sun & Yishu Zeng, 2021. "Characterization of equilibrium existence and purification in general Bayesian games," Papers 2106.08563, arXiv.org.
    8. Bo Chen & Marco Serena, 2020. "Bid Caps and Disclosure Policies," Working Papers tax-mpg-rps-2020-08, Max Planck Institute for Tax Law and Public Finance.
    9. Ivan Pastine & Tuvana Pastine, 2023. "Equilibrium existence and expected payoffs in all-pay auctions with constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(4), pages 983-1007, May.
    10. Vladimir Petkov, 2023. "Prize formation and sharing in multi-stage contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(1), pages 259-289, January.
    11. 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.
    12. Shanglyu Deng & Hanming Fang & Qiang Fu & Zenan Wu, 2020. "Confidence Management in Tournaments," NBER Working Papers 27186, National Bureau of Economic Research, Inc.
    13. Llorente-Saguer, Aniol & Sheremeta, Roman M. & Szech, Nora, 2023. "Designing contests between heterogeneous contestants: An experimental study of tie-breaks and bid-caps in all-pay auctions," European Economic Review, Elsevier, vol. 154(C).
    14. Subhasish M. Chowdhury & Patricia Esteve‐González & Anwesha Mukherjee, 2023. "Heterogeneity, leveling the playing field, and affirmative action in contests," Southern Economic Journal, John Wiley & Sons, vol. 89(3), pages 924-974, January.
    15. 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).
    16. Letina, Igor & Liu, Shuo & Netzer, Nick, 2020. "Delegating performance evaluation," Theoretical Economics, Econometric Society, vol. 15(2), May.
    17. Llorente-Saguer, Aniol & Sheremeta, Roman & Szech, Nora, 2016. "Designing Contests Between Heterogeneous Contestants: An Experimental Study of Tie-Breaks and Bid-Caps in All-Pay Auctions," MPRA Paper 71202, University Library of Munich, Germany.
    18. Nessah, Rabia & Tian, Guoqiang, 2008. "Existence of Equilibria in Discontinuous Games," MPRA Paper 41206, University Library of Munich, Germany, revised Mar 2010.
    19. Cohen, Chen & Levi, Ofer & Sela, Aner, 2019. "All-pay auctions with asymmetric effort constraints," Mathematical Social Sciences, Elsevier, vol. 97(C), pages 18-23.
    20. Correia-da-Silva, João, 2020. "Self-rejecting mechanisms," Games and Economic Behavior, Elsevier, vol. 120(C), pages 434-457.

    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:eee:mateco:v:104:y:2023:i:c:s0304406822001306. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    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.