IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2505.03291.html
   My bibliography  Save this paper

Simultaneous All-Pay Auctions with Budget Constraints

Author

Listed:
  • Yan Liu
  • Ying Qin
  • Zihe Wang

Abstract

The all-pay auction, a classic competitive model, is widely applied in scenarios such as political elections, sports competitions, and research and development, where all participants pay their bids regardless of winning or losing. However, in the traditional all-pay auction, players have no budget constraints, whereas in real-world scenarios, players typically face budget constraints. This paper studies the Nash equilibrium of two players with budget constraints across multiple heterogeneous items in a complete-information framework. The main contributions are as follows: (1) a comprehensive characterization of the Nash equilibrium in single-item auctions with asymmetric budgets and valuations; (2) the construction of a joint distribution Nash equilibrium for the two-item scenario; and (3) the construction of a joint distribution Nash equilibrium for the three-item scenario. Unlike the unconstrained all-pay auction, which always has a Nash equilibrium, a Nash equilibrium may not exist when players have budget constraints. Our findings highlight the intricate effects of budget constraints on bidding strategies, providing new perspectives and methodologies for theoretical analysis and practical applications of all-pay auctions.

Suggested Citation

  • Yan Liu & Ying Qin & Zihe Wang, 2025. "Simultaneous All-Pay Auctions with Budget Constraints," Papers 2505.03291, arXiv.org.
    • Handle: RePEc:arx:papers:2505.03291
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2505.03291
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Arye L. Hillman & John G. Riley, 1989. "Politically Contestable Rents And Transfers," Economics and Politics, Wiley Blackwell, vol. 1(1), pages 17-39, March.
    2. Dan Kovenock & Brian Roberson, 2021. "Generalizations of the General Lotto and Colonel Blotto games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 997-1032, April.
    3. Barut, Yasar & Kovenock, Dan, 1998. "The symmetric multiple prize all-pay auction with complete information," European Journal of Political Economy, Elsevier, vol. 14(4), pages 627-644, November.
    4. Uwe Dulleck & Paul Frijters & Konrad Podczeck, 2006. "All-pay auctions with budget constraints and fair insurance," Economics working papers 2006-13, Department of Economics, Johannes Kepler University Linz, Austria.
    5. Uwe Dulleck & Paul Frijters & Konrad Podczeck, 2006. "All-pay auctions with budget constraints and fair insurance," Economics working papers 2006-13, Department of Economics, Johannes Kepler University Linz, Austria.
    6. Eddie Dekel & Matthew Jackson & Asher Wolinsky, 2007. "Jump Bidding and Budget Constraints in All-Pay Auctions and Wars of Attrition," Discussion Papers 1454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. Barry J. Nalebuff & Joseph E. Stiglitz, 1983. "Prices and Incentives: Towards a General Theory of Compensation and Competition," Bell Journal of Economics, The RAND Corporation, vol. 14(1), pages 21-43, Spring.
    8. Hwang, Sung-Ha & Koh, Youngwoo & Lu, Jingfeng, 2023. "Constrained contests with a continuum of battles," Games and Economic Behavior, Elsevier, vol. 142(C), pages 992-1011.
    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. Emmanuel Dechenaux & Dan Kovenock & Roman Sheremeta, 2015. "A survey of experimental research on contests, all-pay auctions and tournaments," Experimental Economics, Springer;Economic Science Association, vol. 18(4), pages 609-669, December.
    2. Pradeep Dubey & Siddhartha Sahi, 2016. "Optimal Prizes," Department of Economics Working Papers 16-03, Stony Brook University, Department of Economics.
    3. Pradeep Dubey & Siddhartha Sahi, 2009. "The Allocation of a Prize," Department of Economics Working Papers 09-01, Stony Brook University, Department of Economics.
    4. Bastani, Spencer & Giebe, Thomas & Gürtler, Oliver, 2019. "A general framework for studying contests," MPRA Paper 97363, University Library of Munich, Germany.
    5. Konrad, Kai A., 2007. "Strategy in contests: an introduction [Strategie in Turnieren – eine Einführung]," Discussion Papers, Research Unit: Market Processes and Governance SP II 2007-01, WZB Berlin Social Science Center.
    6. Minchuk, Yizhaq & Sela, Aner, 2014. "All-pay auctions with certain and uncertain prizes," Games and Economic Behavior, Elsevier, vol. 88(C), pages 130-134.
    7. Drugov, Mikhail & Ryvkin, Dmitry, 2020. "Tournament rewards and heavy tails," Journal of Economic Theory, Elsevier, vol. 190(C).
    8. Benny Moldovanu & Aner Sela, 2008. "The Optimal Allocation of Prizes in Contests," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 615-631, Springer.
    9. Aner Sela, 2012. "Sequential two-prize contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(2), pages 383-395, October.
    10. Pradeep Dubey & Siddhartha Sah, 2012. "The Allocation of a Prize (Expanded)," Department of Economics Working Papers 12-02, Stony Brook University, Department of Economics.
    11. Robert Akerlof & Richard Holden, 2012. "The nature of tournaments," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(2), pages 289-313, October.
    12. Bastani, Spencer & Giebe, Thomas & Gürtler, Oliver, 2022. "Simple equilibria in general contests," Games and Economic Behavior, Elsevier, vol. 134(C), pages 264-280.
    13. Segev, Ella & Sela, Aner, 2014. "Sequential all-pay auctions with noisy outputs," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 251-261.
    14. Moldovanu, Benny & Sela, Aner, 2006. "Contest architecture," Journal of Economic Theory, Elsevier, vol. 126(1), pages 70-96, January.
    15. Kamijo, Yoshio, 2016. "Rewards versus punishments in additive, weakest-link, and best-shot contests," Journal of Economic Behavior & Organization, Elsevier, vol. 122(C), pages 17-30.
    16. Marco Faravelli, 2011. "The Important Thing Is Not (Always) Winning but Taking Part: Funding Public Goods with Contests," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 13(1), pages 1-22, February.
    17. Denter, Philipp & Sisak, Dana, 2015. "Do polls create momentum in political competition?," Journal of Public Economics, Elsevier, vol. 130(C), pages 1-14.
    18. Cohen, Chen & Lagziel, David & Levi, Ofer & Sela, Aner, 2023. "The role of the second prize in all-pay auctions with two heterogeneous prizes," Journal of Mathematical Economics, Elsevier, vol. 105(C).
    19. Jia, Hao & Skaperdas, Stergios & Vaidya, Samarth, 2013. "Contest functions: Theoretical foundations and issues in estimation," International Journal of Industrial Organization, Elsevier, vol. 31(3), pages 211-222.
    20. Matthias Kräkel, 2006. "Splitting Leagues," Journal of Economics, Springer, vol. 88(1), pages 21-48, June.

    More about this item

    Statistics

    Access and download statistics

    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:arx:papers:2505.03291. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.