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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.

Suggested Citation

  • Cao, Xiaoyong & Tian, Guoqiang, 2012. "Second-Price Auctions with Different Participation Costs," MPRA Paper 41200, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:41200
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    References listed on IDEAS

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    1. Kaplan, Todd & Sela, Aner, 2003. "Auctions with Private Entry Costs," CEPR Discussion Papers 4080, C.E.P.R. Discussion Papers.
    2. Campbell, Colin M., 1998. "Coordination in Auctions with Entry," Journal of Economic Theory, Elsevier, vol. 82(2), pages 425-450, October.
    3. 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.
    4. Tan, Guofu & Yilankaya, Okan, 2006. "Equilibria in second price auctions with participation costs," Journal of Economic Theory, Elsevier, vol. 130(1), pages 205-219, September.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
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    Citations

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    Cited by:

    1. Jinhyuk Lee & Jaeok Park, 2016. "Second-price auctions with sequential and costly participation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(3), pages 567-586, August.
    2. Celik, Gorkem & Yilankaya, Okan, 2017. "Resale in second-price auctions with costly participation," International Journal of Industrial Organization, Elsevier, vol. 54(C), pages 148-174.
    3. Lorentziadis, Panos L., 2016. "Optimal bidding in auctions from a game theory perspective," European Journal of Operational Research, Elsevier, vol. 248(2), pages 347-371.
    4. repec:spr:joecth:v:65:y:2018:i:2:d:10.1007_s00199-016-1028-6 is not listed on IDEAS
    5. Xiaoyong Cao & Guofu Tan & Guoqiang Tian & Okan Yilankaya, 2018. "Equilibria in second-price auctions with private participation costs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(2), pages 231-249, March.

    More about this item

    Keywords

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

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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