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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
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    Citations

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    Cited by:

    1. Kai A. Konrad & Dan Kovenock, 2022. "Introduction to the Special Issue on Contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(4), pages 1017-1023, November.
    2. Franke, Jörg & Metzger, Lars P., 2023. "Repeated Contests with Draws," Ruhr Economic Papers 1016, 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," CESifo Working Paper Series 2744, CESifo.
    4. Eitan Sapiro-Gheiler, 2024. "Persuasion with ambiguous receiver preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(4), pages 1173-1218, June.
    5. 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.
    6. Gadi Fibich & Arieh Gavious & Aner Sela, 2004. "All-Pay Auctions with Weakly Risk-Averse Buyers," Working Papers 2004.14, Fondazione Eni Enrico Mattei.
    7. 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.

    More about this item

    Keywords

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    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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