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All-pay auctions with ties

Author

Listed:
  • Alan Gelder

    (Institute for Defense Analyses)

  • Dan Kovenock

    (Chapman University)

  • Brian Roberson

    (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. Players thus 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, 2022. "All-pay auctions with ties," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(4), pages 1183-1231, November.
    • Handle: RePEc:spr:joecth:v:74:y:2022:i:4:d:10.1007_s00199-019-01195-7
    DOI: 10.1007/s00199-019-01195-7
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    1. 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.
    2. Szech, Nora, 2015. "Tie-breaks and bid-caps in all-pay auctions," Games and Economic Behavior, Elsevier, vol. 92(C), pages 138-149.
    3. 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.
    4. 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.
    5. 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.
    6. Gong, Jiong & Li, Jianpei & McAfee, R. Preston, 2012. "Split-award contracts with investment," Journal of Public Economics, Elsevier, vol. 96(1), pages 188-197.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Cohen Chen & Sela Aner, 2007. "Contests with Ties," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 7(1), pages 1-18, December.
    12. Imhof, Lorens & Kräkel, Matthias, 2014. "Tournaments with gaps," Economics Letters, Elsevier, vol. 122(2), pages 211-214.
    13. Szech, Nora & Weinschenk, Philipp, 2013. "Rebates in a Bertrand game," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 124-133.
    14. 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.
    15. 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.
    16. 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.
    17. Maya Eden, 2006. "Optimal Ties in Contests," Discussion Paper Series dp430, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    18. Arye L. Hillman & John G. Riley, 1989. "Politically Contestable Rents And Transfers," Economics and Politics, Wiley Blackwell, vol. 1(1), pages 17-39, March.
    19. Yeon-Koo Che & Ian Gale, 2003. "Optimal Design of Research Contests," American Economic Review, American Economic Association, vol. 93(3), pages 646-671, June.
    20. Gelder, Alan & Kovenock, Dan & Sheremeta, Roman, 2015. "Behavior in All-Pay Auctions with Ties," MPRA Paper 67517, University Library of Munich, Germany.
    21. 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.
    22. 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.
    23. Klemperer, Paul D, 1987. "Entry Deterrence in Markets with Consumer Switching Costs," Economic Journal, Royal Economic Society, vol. 97(388a), pages 99-117, Supplemen.
    24. 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.
    25. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603.
    26. 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.
    27. 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.
    28. Shilony, Yuval, 1977. "Mixed pricing in oligopoly," Journal of Economic Theory, Elsevier, vol. 14(2), pages 373-388, April.
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    Citations

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    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.

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    More about this item

    Keywords

    All-pay auction; Contest; Ties; 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

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