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Second-price Auction with Two-Dimensional Private Information on Values and Participation Costs

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  • Cao, Xiaoyong
  • Tian, Guoqiang

Abstract

This paper studies equilibria of second price auctions when values and participation costs are both privation information and are drawn from general distribution functions. We consider the existence and uniqueness of equilibrium. It is shown that there always exists an equilibrium for this general economy, and further there exists a unique symmetric equilibrium when all bidders are ex ante homogenous. Moreover, we identify a sufficient condition under which we have a unique equilibrium in a heterogenous economy with two bidders. Our general framework covers many relevant models in the literature as special cases.

Suggested Citation

  • Cao, Xiaoyong & Tian, Guoqiang, 2007. "Second-price Auction with Two-Dimensional Private Information on Values and Participation Costs," MPRA Paper 41224, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:41224
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    References listed on IDEAS

    as
    1. Sela, Aner & Kaplan, Todd, 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. Samuelson, William F., 1985. "Competitive bidding with entry costs," Economics Letters, Elsevier, vol. 17(1-2), pages 53-57.
    5. Olivier Compte & Philippe Jehiel, 2007. "Auctions and information acquisition: sealed bid or dynamic formats?," RAND Journal of Economics, RAND Corporation, vol. 38(2), pages 355-372, June.
    6. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    7. Harstad, Ronald M, 1990. "Alternative Common-Value Auction Procedures: Revenue Comparisons with Free Entry," Journal of Political Economy, University of Chicago Press, vol. 98(2), pages 421-429, April.
    8. Blume, Andreas & Heidhues, Paul, 2004. "All equilibria of the Vickrey auction," Journal of Economic Theory, Elsevier, vol. 114(1), pages 170-177, January.
    9. 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.
    10. 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.
    11. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
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    Cited by:

    1. Tian, Guoqiang & Xiao, Mingjun, 2009. "Vickrey Auctions with Sequential and Costly Participation," MPRA Paper 41203, University Library of Munich, Germany.

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    More about this item

    Keywords

    Two-Dimensional types; Private Values; Private Participation Costs; Second Price Auctions; Existence and Uniqueness of Equilibrium;
    All these keywords.

    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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