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The All‐Pay Auction with Nonmonotonic Payoff

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  • Subhasish M. Chowdhury

Abstract

I model innovation contests as an all‐pay auction in which it is possible not to achieve successful innovation despite costly R&D investments, and as a result, there is no winner. In such a case, the winning payoff turns out to be nonmonotonic in own bid. I derive the sufficient conditions for the existence of pure strategy equilibria, and fully characterize the nondegenerate mixed strategy equilibrium. In the mixed strategy equilibrium, the support of the low‐value bidder is not continuous, and both the high‐value and the low‐value bidders place an atom in the (distinct) lower bound of their respective support. Under symmetric valuation, both bidders place an atom at zero. These results can explain why one does not observe very low quality innovation in real life, or why even symmetric firms may stay out of an innovation contest.

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  • Subhasish M. Chowdhury, 2017. "The All‐Pay Auction with Nonmonotonic Payoff," Southern Economic Journal, John Wiley & Sons, vol. 84(2), pages 375-390, October.
    • Handle: RePEc:wly:soecon:v:84:y:2017:i:2:p:375-390
    DOI: 10.1002/soej.12229
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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.
    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. 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

    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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