IDEAS home Printed from https://ideas.repec.org/p/chu/wpaper/16-31.html
   My bibliography  Save this paper

All-Pay Auctions with Ties

Author

Listed:
  • Alan Gelder

    (Institute for Defense Analyses)

  • Dan Kovenock

    (Economic Science Institute, Chapman University)

  • Brian Roberson

    (Department of Economics, Purdue University)

Abstract

We study the two-player, complete information all-pay auction in which a tie ensues if neither player outbids the other by more than a given amount. In the event of a tie, each player receives an identical fraction of the winning prize. Thus players engage in two margins of competition: losing versus tying, and tying versus winning. Two pertinent parameters are the margin required for victory and the value of tying relative to winning. We fully characterize the set of Nash equilibria for the entire parameter space. For much of the parameter space, there is a unique Nash equilibrium which is also symmetric. Equilibria typically involve randomizing over multiple disjoint intervals, so that in essence players randomize between attempting to tie and attempting to win. In equilibrium, expected bids and payoffs are non-monotonic in both the margin required for victory and the relative value of tying.

Suggested Citation

  • Alan Gelder & Dan Kovenock & Brian Roberson, 2016. "All-Pay Auctions with Ties," Working Papers 16-31, Chapman University, Economic Science Institute.
    • Handle: RePEc:chu:wpaper:16-31
    as

    Download full text from publisher

    File URL: http://www.chapman.edu/research-and-institutions/economic-science-institute/_files/WorkingPapers/All-Pay-Auctions-with-Ties-2016.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Maya Eden, 2006. "Optimal Ties in Contests," Discussion Paper Series dp430, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    2. Lazear, Edward P & Rosen, Sherwin, 1981. "Rank-Order Tournaments as Optimum Labor Contracts," Journal of Political Economy, University of Chicago Press, vol. 89(5), pages 841-864, October.
    3. Szech, Nora, 2015. "Tie-breaks and bid-caps in all-pay auctions," Games and Economic Behavior, Elsevier, vol. 92(C), pages 138-149.
    4. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603.
    5. Arye L. Hillman & John G. Riley, 1989. "Politically Contestable Rents And Transfers," Economics and Politics, Wiley Blackwell, vol. 1(1), pages 17-39, March.
    6. 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.
    7. Paul Klemperer, 1987. "Markets with Consumer Switching Costs," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(2), pages 375-394.
    8. Christian Ewerhart, 2015. "Mixed equilibria in Tullock contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(1), pages 59-71, September.
    9. Yeon-Koo Che & Ian Gale, 2003. "Optimal Design of Research Contests," American Economic Review, American Economic Association, vol. 93(3), pages 646-671, June.
    10. Che, Yeon-Koo & Gale, Ian, 2000. "Difference-Form Contests and the Robustness of All-Pay Auctions," Games and Economic Behavior, Elsevier, vol. 30(1), pages 22-43, January.
    11. Dan Kovenock & Raymond J. Deneckere, 1996. "Bertrand-Edgeworth duopoly with unit cost asymmetry (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 1-25.
    12. Gong, Jiong & Li, Jianpei & McAfee, R. Preston, 2012. "Split-award contracts with investment," Journal of Public Economics, Elsevier, vol. 96(1), pages 188-197.
    13. 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.
    14. Gelder, Alan & Kovenock, Dan & Sheremeta, Roman, 2015. "Behavior in All-Pay Auctions with Ties," MPRA Paper 67517, University Library of Munich, Germany.
    15. Imhof, Lorens & Kräkel, Matthias, 2014. "Tournaments with gaps," Economics Letters, Elsevier, vol. 122(2), pages 211-214.
    16. Peter Postl, 2013. "Efficiency versus optimality in procurement," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(2), pages 425-472, June.
    17. Fisher, Eric ON. & Wilson, Charles A., 1995. "Price competition between two international firms facing tariffs," International Journal of Industrial Organization, Elsevier, vol. 13(1), pages 67-87, March.
    18. Anton, James J. & Brusco, Sandro & Lopomo, Giuseppe, 2010. "Split-award procurement auctions with uncertain scale economies: Theory and data," Games and Economic Behavior, Elsevier, vol. 69(1), pages 24-41, May.
    19. Shilony, Yuval, 1977. "Mixed pricing in oligopoly," Journal of Economic Theory, Elsevier, vol. 14(2), pages 373-388, April.
    20. Baye, Michael R & Kovenock, Dan & de Vries, Casper G, 1994. "The Solution to the Tullock Rent-Seeking Game When R Is Greater Than 2: Mixed-Strategy Equilibria and Mean Dissipation Rates," Public Choice, Springer, vol. 81(3-4), pages 363-380, December.
    21. Cohen Chen & Sela Aner, 2007. "Contests with Ties," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 7(1), pages 1-18, December.
    22. Osborne, Martin J. & Pitchik, Carolyn, 1986. "Price competition in a capacity-constrained duopoly," Journal of Economic Theory, Elsevier, vol. 38(2), pages 238-260, April.
    23. Aadhaar Chaturvedi & Damian R. Beil & Victor Martínez-de-Albéniz, 2014. "Split-Award Auctions for Supplier Retention," Management Science, INFORMS, vol. 60(7), pages 1719-1737, July.
    24. Szech, Nora & Weinschenk, Philipp, 2013. "Rebates in a Bertrand game," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 124-133.
    25. 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.
    26. Klemperer, Paul D, 1987. "Entry Deterrence in Markets with Consumer Switching Costs," Economic Journal, Royal Economic Society, vol. 97(388a), pages 99-117, Supplemen.
    27. Hao Jia, 2012. "Contests with the Probability of a Draw: A Stochastic Foundation," The Economic Record, The Economic Society of Australia, vol. 88(282), pages 391-406, September.
    28. Blavatskyy, Pavlo R., 2010. "Contest success function with the possibility of a draw: Axiomatization," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 267-276, March.
    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. Bettina Klose & Dan Kovenock, 2015. "Extremism drives out moderation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(4), pages 861-887, April.
    2. Franke, Jörg & Kanzow, Christian & Leininger, Wolfgang & Väth, Alexandra, 2009. "Effort Maximization in Asymmetric N-person Contest Games," Ruhr Economic Papers 130, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    3. Jörg Franke & Christian Kanzow & Wolfgang Leininger & Alexandra Väth, 2009. "Effort Maximization in Asymmetric N-person Contest Games," Ruhr Economic Papers 0130, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    4. repec:zbw:rwirep:0130 is not listed on IDEAS
    5. Gadi Fibich & Arieh Gavious & Aner Sela, 2004. "All-Pay Auctions with Weakly Risk-Averse Buyers," Working Papers 2004.14, Fondazione Eni Enrico Mattei.

    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. Alan Gelder & Dan Kovenock & Roman Sheremeta, 2015. "Behavior in All-Pay Auctions with Ties," Working Papers 15-22, Chapman University, Economic Science Institute.
    2. Alberto Vesperoni, 2016. "A contest success function for rankings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(4), pages 905-937, December.
    3. Li, Bo & Wu, Zenan & Xing, Zeyu, 2023. "Optimally biased contests with draws," Economics Letters, Elsevier, vol. 226(C).
    4. 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).
    5. 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.
    6. Goel, Sumit & Goyal, Amit, 2023. "Optimal tie-breaking rules," Journal of Mathematical Economics, Elsevier, vol. 108(C).
    7. 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.
    8. Subhasish Chowdhury & Roman Sheremeta, 2015. "Strategically equivalent contests," Theory and Decision, Springer, vol. 78(4), pages 587-601, April.
    9. Ewerhart, Christian, 2017. "Contests with small noise and the robustness of the all-pay auction," Games and Economic Behavior, Elsevier, vol. 105(C), pages 195-211.
    10. 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.
    11. 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.
    12. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.
    13. Roman M. Sheremeta, 2016. "The pros and cons of workplace tournaments," IZA World of Labor, Institute of Labor Economics (IZA), pages 302-302, October.
    14. Lian Jian & Zheng Li & Tracy Xiao Liu, 2017. "Simultaneous versus sequential all-pay auctions: an experimental study," Experimental Economics, Springer;Economic Science Association, vol. 20(3), pages 648-669, September.
    15. Morgan, John & Tumlinson, Justin & Várdy, Felix, 2022. "The limits of meritocracy," Journal of Economic Theory, Elsevier, vol. 201(C).
    16. Segev, Ella & Sela, Aner, 2014. "Sequential all-pay auctions with noisy outputs," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 251-261.
    17. Pradeep Dubey & Siddhartha Sahi, 2016. "Optimal Prizes," Department of Economics Working Papers 16-03, Stony Brook University, Department of Economics.
    18. Feng, Xin & Lu, Jingfeng, 2018. "How to split the pie: Optimal rewards in dynamic multi-battle competitions," Journal of Public Economics, Elsevier, vol. 160(C), pages 82-95.
    19. HHironori Otsubo, 2012. "Contests with Incumbency Advantages: An Experiment Investigation of the Effect of Limits on Spending Behavior and Outcome," Jena Economics Research Papers 2012-020, Friedrich-Schiller-University Jena.
    20. Ewerhart, Christian & Sun, Guang-Zhen, 2024. "The n-player Hirshleifer contest," Games and Economic Behavior, Elsevier, vol. 143(C), pages 300-320.

    More about this item

    Keywords

    All-pay auction; contest; tie; draws; bid differential;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:chu:wpaper:16-31. 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: Megan Luetje (email available below). General contact details of provider: https://edirc.repec.org/data/esichus.html .

    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.