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Competing auctions: finite markets and convergence

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    (Department of Economics, University of Rochester)

Abstract

The literature on competing auctions offers a model where sellers compete for buyers by setting reserve prices freely. An important outstanding conjecture (e.g. Peters and Severinov (1997)) is that the sellers post prices close to their marginal costs when the market becomes large. This conjecture is confirmed in this paper. More precisely, we show that if all sellers have zero costs, then the equilibrium reserve price converges to 0 in distribution. I also show that if there is a high enough lower bound on the buyers’ valuations, then there is a symmetric pure strategy equilibrium. In this equilibrium, if the number of buyers (sellers) increases, then the equilibrium reserve price increases (decreases) and the reserve price is decreasing in the size of the market.

Suggested Citation

  • ,, 2010. "Competing auctions: finite markets and convergence," Theoretical Economics, Econometric Society, vol. 5(2), May.
    • Handle: RePEc:the:publsh:538
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    Citations

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    Cited by:

    1. Lester, Benjamin & Visschers, Ludo & Wolthoff, Ronald, 2015. "Meeting technologies and optimal trading mechanisms in competitive search markets," Journal of Economic Theory, Elsevier, vol. 155(C), pages 1-15.
    2. Cristián Troncoso-Valverde, 2018. "Releasing information in private-value second-price auctions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(3), pages 781-817, May.
    3. Attar, Andrea & Campioni, Eloisa & Piaser, Gwenaël, 2018. "On competing mechanisms under exclusive competition," Games and Economic Behavior, Elsevier, vol. 111(C), pages 1-15.
    4. Hafalir, Isa E. & Hakimov, Rustamdjan & Kübler, Dorothea & Kurino, Morimitsu, 2018. "College admissions with entrance exams: Centralized versus decentralized," Journal of Economic Theory, Elsevier, vol. 176(C), pages 886-934.
    5. Han, Seungjin, 2015. "Robust competitive auctions," Economics Letters, Elsevier, vol. 136(C), pages 207-210.
    6. Virág, Gábor, 2011. "High profit equilibria in directed search models," Games and Economic Behavior, Elsevier, vol. 71(1), pages 224-234, January.
    7. Forand, Jean Guillaume, 2013. "Competing through information provision," International Journal of Industrial Organization, Elsevier, vol. 31(5), pages 438-451.
    8. Maslov, Alexander & Schwartz, Jesse A., 2022. "Imperfect competition in online auctions," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    9. Damian Damianov, 2012. "Seller competition by mechanism design," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(1), pages 105-137, September.
    10. Han, Seungjin, 2022. "General competing mechanism games with strategy-proof punishment," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    11. Backus, Matthew R. & Podwol, Joseph Uri & Schneider, Henry S., 2014. "Search costs and equilibrium price dispersion in auction markets," European Economic Review, Elsevier, vol. 71(C), pages 173-192.
    12. Feess, Eberhard & Grund, Christian & Walzl, Markus & Wohlschlegel, Ansgar, 2020. "Competing trade mechanisms and monotone mechanism choice," European Journal of Operational Research, Elsevier, vol. 280(3), pages 1108-1121.
    13. Carvajal, Andrés & Thereze, João, 2023. "Insurance contracts and financial markets," Mathematical Social Sciences, Elsevier, vol. 121(C), pages 8-19.
    14. Podwol, Joseph Uri & Schneider, Henry S., 2016. "Nonstandard bidder behavior in real-world auctions," European Economic Review, Elsevier, vol. 83(C), pages 198-212.

    More about this item

    Keywords

    Competing auctions; finite markets; convergence;
    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
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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