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Second-Price Auctions with Different Participation Costs

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  • Cao, Xiaoyong
  • Tian, Guoqiang

Abstract

This paper studies equilibria of second price auctions in independent private value envi- ronments with different participation costs. Two types of equilibria are identified: monotonic equilibria in which a bidder with a lower participation cost results in a lower cutoff for sub- mitting a bid, and non-monotonic equilibria in which a lower participation cost results in a higher cutoff. We show that there always exists a monotonic equilibrium, and further, that the monotonic equilibrium is unique for either concave distribution functions or strictly convex distribution functions with non-increasing reverse hazard rates. There exist non- monotonic equilibria when the distribution functions are strictly convex and the difference of the participation costs is sufficiently small. We also provide comparative static analysis and study the limiting properties of equilibria when the difference in bidders’ participation costs approaches zero.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 41200.

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Date of creation: 01 Feb 2012
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Handle: RePEc:pra:mprapa:41200

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Keywords: Private Values; Differentiated Participation Costs; Second Price Auctions; Non-monotonic Equilibrium; Existence and Uniqueness of Equilibrium;

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  1. Harstad, Ronald M. & Kagel, John H. & Levin, Dan, 1990. "Equilibrium bid functions for auctions with an uncertain number of bidders," Economics Letters, Elsevier, vol. 33(1), pages 35-40, May.
  2. Campbell, Colin M., 1998. "Coordination in Auctions with Entry," Journal of Economic Theory, Elsevier, vol. 82(2), pages 425-450, October.
  3. Kaplan, Todd & Sela, Aner, 2003. "Auctions with Private Entry Costs," CEPR Discussion Papers 4080, C.E.P.R. Discussion Papers.
  4. Tan, Guofu & Yilankaya, Okan, 2004. "Equilibria in Second Price Auctions with Participation Costs," Microeconomics.ca working papers tan-04-01-24-10-08-06, Vancouver School of Economics, revised 09 Jun 2006.
  5. McAfee, R. Preston & McMillan, John, 1987. "Auctions with a stochastic number of bidders," Journal of Economic Theory, Elsevier, vol. 43(1), pages 1-19, October.
  6. Engelbrecht-Wiggans, Richard, 2001. "The effect of entry and information costs on oral versus sealed-bid auctions," Economics Letters, Elsevier, vol. 70(2), pages 195-202, February.
  7. Miralles, Antonio, 2008. "Intuitive and noncompetitive equilibria in weakly efficient auctions with entry costs," Mathematical Social Sciences, Elsevier, vol. 56(3), pages 448-455, November.
  8. Cao, Xiaoyong & Tian, Guoqiang, 2010. "Equilibria in first price auctions with participation costs," Games and Economic Behavior, Elsevier, vol. 69(2), pages 258-273, July.
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