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Nash equilibria in all-pay auctions with discrete strategy space

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  • Li, Zheng

Abstract

Using two-player all-pay auctions, the author fully characterizes the Nash equilibrium under a discrete bidding strategy space. In particular, he shows that under the random tiebreaking rule, the cardinality of the set of Nash equilibrium depends on the parity of the reward size and a continuum of Nash equilibria exists. Additionally, when a simple favorone-sided tie-breaking rule is used, the equilibrium solution becomes independent of the reward size.

Suggested Citation

  • Li, Zheng, 2017. "Nash equilibria in all-pay auctions with discrete strategy space," Economics Discussion Papers 2017-22, Kiel Institute for the World Economy (IfW Kiel).
    • Handle: RePEc:zbw:ifwedp:201722
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    References listed on IDEAS

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    1. Michael R. Baye & Dan Kovenock & Casper G. Vries, 2008. "Rigging the lobbying process: An application of the all-pay auction," Springer Books, in: Roger D. Congleton & Kai A. Konrad & Arye L. Hillman (ed.), 40 Years of Research on Rent Seeking 2, pages 331-336, Springer.
    2. 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.
    3. Cohen Chen & Sela Aner, 2007. "Contests with Ties," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 7(1), pages 1-18, December.
    4. Arye L. Hillman & John G. Riley, 1989. "Politically Contestable Rents And Transfers," Economics and Politics, Wiley Blackwell, vol. 1(1), pages 17-39, March.
    5. James Boudreau, 2011. "All-pay auctions with discrete action spaces," Applied Economics Letters, Taylor & Francis Journals, vol. 18(2), pages 161-162.
    6. Hironori Otsubo, 2015. "Nash Equilibria in a Two-Person Discrete All-Pay Auction with Unfair Tie-Break and Complete Information," Economics Bulletin, AccessEcon, vol. 35(4), pages 245-245.
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    Cited by:

    1. Itzhak Rasooly & Carlos Gavidia-Calderon, 2020. "The importance of being discrete: on the inaccuracy of continuous approximations in auction theory," Papers 2006.03016, arXiv.org, revised Aug 2022.

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    More about this item

    Keywords

    asymmetric Nash equilibrium; all-pay auction;

    JEL classification:

    • 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

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