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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].

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 141 (2008)
Issue (Month): 1 (July)
Pages: 1-27

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Handle: RePEc:eee:jetheo:v:141:y:2008:i:1:p:1-27

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Web page: http://www.elsevier.com/locate/inca/622869

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  1. MINGLI ZHENG & Robert McMillan & SAJID ANWAR, 2005. "Bidding Behavior in Competing Auctions: Evidence from eBay," Microeconomics 0505001, EconWPA.
  2. McAfee, R Preston, 1993. "Mechanism Design by Competing Sellers," Econometrica, Econometric Society, vol. 61(6), pages 1281-1312, November.
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  17. Peters, Michael & Severinov, Sergei, 2006. "Internet auctions with many traders," Journal of Economic Theory, Elsevier, vol. 130(1), pages 220-245, September.
  18. Robert G. Hansen, 1988. "Auctions with Endogenous Quantity," RAND Journal of Economics, The RAND Corporation, vol. 19(1), pages 44-58, Spring.
  19. Peters, Michael & Severinov, Sergei, 1997. "Competition among Sellers Who Offer Auctions Instead of Prices," Journal of Economic Theory, Elsevier, vol. 75(1), pages 141-179, July.
  20. Burguet, Roberto & Sakovics, Jozsef, 1999. "Imperfect Competition in Auction Designs," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(1), pages 231-47, February.
  21. Carl Davidson & Raymond Deneckere, 1986. "Long-Run Competition in Capacity, Short-Run Competition in Price, and the Cournot Model," RAND Journal of Economics, The RAND Corporation, vol. 17(3), pages 404-415, Autumn.
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Citations

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Cited by:
  1. Szech, Nora, 2011. "Optimal advertising of auctions," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2596-2607.
  2. Alexander Matros & Andriy Zapechelnyuk, 2010. "Competition of E-Commerce Intermediaries," Working Papers 675, Queen Mary, University of London, School of Economics and Finance.
  3. Andersson, Tommy & Andersson, Christer & Andersson, Fredrik, 2010. "An Empirical Investigation of Efficiency and Price Uniformity in Competing Auctions," Working Papers 2010:14, Lund University, Department of Economics.
  4. 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.
  5. Damian Damianov, 2012. "Seller competition by mechanism design," Economic Theory, Springer, vol. 51(1), pages 105-137, September.
  6. Andrea Attar & Eloisa Campioni & Gwenaël Piaser, 2014. "Competing Mechanisms Communication under Exclusivity Clauses," Working Papers 2014-048, Department of Research, Ipag Business School.

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