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Equilibria in Second Price Auctions with Private Participation Costs


  • Xiaoyong Cao

    () (Department of Economics, University of International Business and Economics, Beijing)

  • Guofu Tan

    () (Department of Economics, University of Southern California)

  • Guoqiang Tian

    () (Department of Economics, Texas A&M University)

  • Okan Yilankaya

    () (Department of Economics, Koc University)


We study equilibria in second price auctions when bidders are independently and privately informed about both their values and participation costs and their joint distributions across bidders are not necessarily identical. We show that there always exists an equilibrium in this general setting with two dimensional types of ex ante heterogeneous bidders. We provide conditions under which the equilibrium is unique. Moreover, when the bidders are ex ante symmetric, we show that there is a unique symmetric equilibrium. We also identify sufficient conditions for existence of asymmetric equilibria.

Suggested Citation

  • Xiaoyong Cao & Guofu Tan & Guoqiang Tian & Okan Yilankaya, 2014. "Equilibria in Second Price Auctions with Private Participation Costs," Koç University-TUSIAD Economic Research Forum Working Papers 1421, Koc University-TUSIAD Economic Research Forum.
  • Handle: RePEc:koc:wpaper:1421

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    References listed on IDEAS

    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. 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.
    4. 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.
    5. Celik Gorkem & Yilankaya Okan, 2009. "Optimal Auctions with Simultaneous and Costly Participation," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-33, July.
    6. Stegeman, Mark, 1996. "Participation Costs and Efficient Auctions," Journal of Economic Theory, Elsevier, vol. 71(1), pages 228-259, October.
    7. Xiaoyong Cao & Guoqiang Tian, 2013. "Second-Price Auctions with Different Participation Costs," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 22(1), pages 184-205, March.
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    More about this item


    Two-Dimensional Types; Private Participation Costs; Second Price Auctions; Existence and Uniqueness of Equilibrium.;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • 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

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