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The All-Pay Auction with Non-Monotonic Payoff

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  • Subhasish Modak Chowdhury

    (Centre for Competition Policy, School of Economics and Centre for Behavioural and Experimental Social Sciences, University of East Anglia)

Abstract

We analyse an endogenous prize all-pay auction under complete information where it is possible that none of the bidders wins and the winning payoff becomes non-monotonic in own bid. We derive the conditions for the existence of pure strategy equilibria and fully characterize the unique mixed strategy equilibrium when pure strategy equilibria do not exist. The highvaluation bidder places two distinct mass points in his equilibrium mixed strategy and the equilibrium support of the low-valuation bidder is not continuous. Under common valuation, in the equilibrium mixed strategy both bidders place mass points at the same point of the support. Possible applications are discussed.

Suggested Citation

  • Subhasish Modak Chowdhury, 2010. "The All-Pay Auction with Non-Monotonic Payoff," Working Paper series, University of East Anglia, Centre for Competition Policy (CCP) 2010-06, Centre for Competition Policy, University of East Anglia, Norwich, UK..
    • Handle: RePEc:uea:ueaccp:2010_06
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    Cited by:

    1. Allison, Blake A. & Bagh, Adib & Lepore, Jason J., 2022. "Invariant equilibria and classes of equivalent games," Games and Economic Behavior, Elsevier, vol. 132(C), pages 448-462.
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    3. Gyoung‐Gyu Choi & Jeong‐Yoo Kim, 2021. "Trade with enemy: Economic interdependence and stability under anarchy," Manchester School, University of Manchester, vol. 89(4), pages 353-366, July.
    4. Ron Siegel, 2014. "Contests with productive effort," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(3), pages 515-523, August.
    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. Duvocelle, Benoit & Mourmans, Niels, 2022. "Contests with discontinuous payoffs," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    7. Hudja, Stanton, 2021. "Is Experimentation Invariant to Group Size? A Laboratory Analysis of Innovation Contests," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 91(C).
    8. Subhasish M. Chowdhury & Debabrata Datta & Souvik Dhar, 2019. "Auction Versus Posted Price Mechanisms in Online Sales: The Roles of Impatience and Dissuasion," Studies in Microeconomics, , vol. 7(1), pages 75-88, June.

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    More about this item

    Keywords

    Contests; All-pay auction; No-win; Non-monotonicity; Pure Strategy;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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