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Competing auctions with endogenous quantities

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  • Moldovanu, Benny
  • Sela, Aner
  • Shi, Xianwen

Abstract

Two sellers decide on their discrete supply of a homogenous good. There is a finite number of buyers with unit demand and privately known valuations. In the first model, there is a centralized market place where a uniform auction takes place. In the second, there are two distinct auction sites, each with one seller, and buyers decide where to bid. Using the theory of potential games, we show that in the one-site auction model there is always an equilibrium in pure-strategies. In contrast, if the distribution of buyers values has an increasing failure rate, and if the marginal cost of production is relatively low, there is no pure-strategy equilibrium where both sellers make positive profits in the competing sites model. We also identify conditions under which an equilibrium with a unique active site exists. We deal with the finite and discrete models by using several results about order statistics developed by Richard Barlow and Frank Proschan [R. Barlow, F. Proschan, Mathematical Theory of Reliability, Wiley, New York, 1965; R. Barlow, F. Proschan, Inequalities for linear combinations of order statistics from restricted families, Ann. Math. Statist. 37 (1966) 1593-1601; R. Barlow, F. Proschan, Statistical Theory of Reliability and Life Testing, McArdle Press, Silver Spring, 1975].

Suggested Citation

  • Moldovanu, Benny & Sela, Aner & Shi, Xianwen, 2008. "Competing auctions with endogenous quantities," Journal of Economic Theory, Elsevier, vol. 141(1), pages 1-27, July.
  • Handle: RePEc:eee:jetheo:v:141:y:2008:i:1:p:1-27
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    References listed on IDEAS

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    Cited by:

    1. Alexander Matros & Andriy Zapechelnyuk, 2010. "Competition of E-Commerce Intermediaries," Working Papers 675, Queen Mary University of London, School of Economics and Finance.
    2. Minchuk, Yizhaq & Sela, Aner, 2014. "All-pay auctions with certain and uncertain prizes," Games and Economic Behavior, Elsevier, vol. 88(C), pages 130-134.
    3. Nikolaus Schweizer & Nora Szech, 2016. "The Quantitative View of Myerson Regularity," CESifo Working Paper Series 5712, CESifo Group Munich.
    4. 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.
    5. Andersson, T. & Andersson, C. & Andersson, F., 2012. "An empirical investigation of efficiency and price uniformity in competing auctions," Economics Letters, Elsevier, vol. 116(1), pages 99-101.
    6. Schweizer, Nikolaus & Szech, Nora, 2015. "The quantitative view of Myerson regularity," Discussion Papers, Research Unit: Economics of Change SP II 2015-307, Social Science Research Center Berlin (WZB).
    7. Ghazala Azmat & Marc Möller, 2009. "Competition among contests," RAND Journal of Economics, RAND Corporation, vol. 40(4), pages 743-768.
    8. Szech, Nora, 2011. "Optimal advertising of auctions," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2596-2607.
    9. Schweizer, Nikolaus & Szech, Nora, 2015. "A quantitative version of Myerson regularity," Working Paper Series in Economics 76, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
    10. repec:ipg:wpaper:2014-048 is not listed on IDEAS
    11. Andrea Attar & Eloisa Campioni & Gwenael Piaser, 2011. "Competing Mechanisms, Exclusive Clauses and the Revelation Principle," CEIS Research Paper 201, Tor Vergata University, CEIS, revised 30 Jun 2011.

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