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Two-bidder all-pay auctions with interdependent valuations, including the highly competitive case

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  • Rentschler, Lucas
  • Turocy, Theodore L.

Abstract

We analyze symmetric, two-bidder all-pay auctions with interdependent valuations and discrete type spaces. Relaxing previous restrictions on the distribution of types and the valuation structure, we present a construction that characterizes all symmetric equilibria. We show how the search problem this construction faces can be complex. In equilibrium, randomization can take place over disjoint intervals of bids, equilibrium supports can have a rich structure, and non-monotonicity of the equilibrium may result in a positive probability of allocative inefficiency when the value of the prize is not common. Particular attention is paid to the case in which an increase in a bidder's posterior expected value of winning the auction is likely to be accompanied by a corresponding increase for the other bidder. Such environments are “highly competitive” in the sense that the bidder's higher valuation also signals that the other bidder has an incentive to bid aggressively.

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  • 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.
    • Handle: RePEc:eee:jetheo:v:163:y:2016:i:c:p:435-466
    DOI: 10.1016/j.jet.2016.02.005
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    Cited by:

    1. Xiao, Jun, 2018. "Equilibrium analysis of the all-pay contest with two nonidentical prizes: Complete results," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 21-34.
    2. Blake A. Allison & Jason J. Lepore, 2024. "Invariant Equilibrium in Discontinuous Bayesian Games," Games, MDPI, vol. 15(3), pages 1-14, May.
    3. Zheng, Charles Z., 2019. "Necessary and sufficient conditions for peace: Implementability versus security," Journal of Economic Theory, Elsevier, vol. 180(C), pages 135-166.
    4. Chi, Chang Koo & Murto, Pauli & Valimaki, Juuso, 2017. "All-Pay Auctions with Affiliated Values," MPRA Paper 80799, University Library of Munich, Germany.
    5. Lu, Jingfeng & Parreiras, Sérgio O., 2017. "Monotone equilibrium of two-bidder all-pay auctions Redux," Games and Economic Behavior, Elsevier, vol. 104(C), pages 78-91.
    6. Doni Nicola & Menicucci Domenico, 2019. "A First Price Auction with an Arbitrary Number of Asymmetric Bidders," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 19(2), pages 1-7, June.
    7. Shanglyu Deng & Hanming Fang & Qiang Fu & Zenan Wu, 2023. "Information Favoritism and Scoring Bias in Contests," PIER Working Paper Archive 23-002, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    8. Prokopovych, Pavlo & Yannelis, Nicholas C., 2023. "On monotone pure-strategy Bayesian-Nash equilibria of a generalized contest," Games and Economic Behavior, Elsevier, vol. 140(C), pages 348-362.
    9. Stefano Barbieri & Kai A. Konrad, 2021. "Overzealous Rule Makers," Journal of Law and Economics, University of Chicago Press, vol. 64(2), pages 341-365.
    10. Diego Aycinena & Rimvydas Baltaduonis & Lucas Rentschler, 2019. "Valuation structure in incomplete information contests: experimental evidence," Public Choice, Springer, vol. 179(3), pages 195-208, June.
    11. Yangguang Huang & Ming He, 2021. "Structural Analysis Of Tullock Contests With An Application To U.S. House Of Representatives Elections," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 62(3), pages 1011-1054, August.
    12. Tracy Xiao Liu, 2018. "All-pay auctions with endogenous bid timing: an experimental study," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 247-271, March.
    13. Jingfeng Lu & Hongkun Ma & Zhe Wang, 2018. "Ranking Disclosure Policies In All‐Pay Auctions," Economic Inquiry, Western Economic Association International, vol. 56(3), pages 1464-1485, July.
    14. Zhuoqiong Chen, 2021. "All-pay auctions with private signals about opponents’ values," Review of Economic Design, Springer;Society for Economic Design, vol. 25(1), pages 33-64, June.
    15. Chi, Chang Koo & Murto, Pauli & Välimäki, Juuso, 2019. "All-pay auctions with affiliated binary signals," Journal of Economic Theory, Elsevier, vol. 179(C), pages 99-130.
    16. Chi, Chang Koo, 2018. "An analysis of the two-bidder all-pay auction with common values," Discussion Paper Series in Economics 17/2018, Norwegian School of Economics, Department of Economics.

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    More about this item

    Keywords

    Contests; All-pay auctions; Mixed strategies;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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