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The all-pay auction with complete information and identity-dependent externalities

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  • Bettina Klose
  • Dan Kovenock

Abstract

We derive a necessary and sufficient condition for the existence of equilibria with only two active players in the all-pay auction with complete information and identity-dependent externalities. This condition shows that the generic equilibrium of the standard all-pay auction is robust to the introduction of "small" identity-dependent externalities. In general, however, the presence of identity-dependent externalities invalidates well-established qualitative results concerning the set of equilibria of the first-price all-pay auction with complete information. With identity-dependent externalities equilibria are generally not payoff equivalent, and identical players may earn different payoffs in equilibrium. These observations show that Siegel’s (2009) results characterizing the set of equilibrium payoffs in all-pay contests, including the all-pay auction as a special case, do not extend to environments with identity-dependent externalities. We further compare the all-pay auction with identity-dependent externalities to the first-price winner-pay auction with identity-dependent externalities. We demonstrate that the equilibrium payoffs of the all-pay auction and winner-pay auction cannot be ranked unambiguously in the presence of identity-dependent externalities by providing examples of environments where equilibrium payoffs in the all-pay auction dominate those in the winner-pay auction and vice versa.

Suggested Citation

  • Bettina Klose & Dan Kovenock, 2013. "The all-pay auction with complete information and identity-dependent externalities," ECON - Working Papers 118, Department of Economics - University of Zurich.
  • Handle: RePEc:zur:econwp:118
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    3. Oliver Kirchkamp & Wladislaw Mill, 2019. "Spite vs. risk: explaining overbidding," CESifo Working Paper Series 7631, CESifo.
    4. Thomas Giebe & Paul Schweinzer, 2014. "All-pay-all aspects of political decision making," Public Choice, Springer, vol. 161(1), pages 73-90, October.
    5. Rentschler, Lucas & Turocy, Theodore L., 2016. "Two-bidder all-pay auctions with interdependent valuations, including the highly competitive case," Journal of Economic Theory, Elsevier, vol. 163(C), pages 435-466.
    6. Stefano Barbieri & Kai A. Konrad, 2021. "Overzealous Rule Makers," Journal of Law and Economics, University of Chicago Press, vol. 64(2), pages 341-365.
    7. Kai A. Konrad & Florian Morath, 2018. "To Deter Or To Moderate? Alliance Formation In Contests With Incomplete Information," Economic Inquiry, Western Economic Association International, vol. 56(3), pages 1447-1463, July.
    8. He, Wei & Yannelis, Nicholas C., 2016. "Existence of equilibria in discontinuous Bayesian games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 181-194.
    9. Henner Gimpel & Valerie Graf-Drasch & Alexander Kammerer & Maximilian Keller & Xinyi Zheng, 2020. "When does it pay off to integrate sustainability in the business model? – A game-theoretic analysis," Electronic Markets, Springer;IIM University of St. Gallen, vol. 30(4), pages 699-716, December.
    10. Prokopovych, Pavlo & Yannelis, Nicholas C., 2014. "On the existence of mixed strategy Nash equilibria," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 87-97.
    11. Aner Sela & Amit Yeshayahu, 2022. "Contests with identity-dependent externalities," Working Papers 2203, Ben-Gurion University of the Negev, Department of Economics.
    12. Bozbay, Irem & Vesperoni, Alberto, 2018. "A contest success function for networks," Journal of Economic Behavior & Organization, Elsevier, vol. 150(C), pages 404-422.
    13. Baik, Kyung Hwan & Jung, Hanjoon Michael, 2021. "Contests with multiple alternative prizes: Public-good/bad prizes and externalities," Journal of Mathematical Economics, Elsevier, vol. 92(C), pages 103-116.
    14. 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.
    15. Aniruddha Bagchi & João Ricardo Faria & Timothy Mathews, 2019. "A model of a multilateral proxy war with spillovers," Public Choice, Springer, vol. 179(3), pages 229-248, June.
    16. Tuvana Pastine & Ivan Pastine, 2021. "Equilibrium Existence and Expected Payoffs in All-Pay Auctions with Constraints," Economics Department Working Paper Series n311-21.pdf, Department of Economics, National University of Ireland - Maynooth.
    17. Kirchkamp, Oliver & Mill, Wladislaw, 2021. "Spite vs. risk: Explaining overbidding in the second-price all-pay auction," Games and Economic Behavior, Elsevier, vol. 130(C), pages 616-635.
    18. Luke A. Boosey & Christopher Brown, 2021. "Contests with Network Externalities: Theory & Evidence," Working Papers wp2021_07_02, Department of Economics, Florida State University.
    19. Mill, Wladislaw & Morgan, John, 2022. "Competition between friends and foes," European Economic Review, Elsevier, vol. 147(C).
    20. Cortes-Corrales, Sebastián & Gorny, Paul M., 2018. "Generalising Conflict Networks," MPRA Paper 90001, University Library of Munich, Germany.

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    More about this item

    Keywords

    All-pay auction; identity-dependent externalities; payoff nonequivalence; political conflict;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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