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Equilibria in Second Price Auctions with Participation Costs


  • Guofu Tan
  • Okan Yilankaya


We investigate equilibria of sealed-bid second price auctions with bidder participation costs in the independent private values environment. We focus on equilibria in cutoff strategies (participate and bid the valuation iff it is greater than the cutoff), since if a bidder finds it optimal to participate, she cannot do better than bidding her valuation. When bidders are symmetric, concavity (strict convexity) of the cumulative distribution function from which the valuations are drawn is a sufficient condition for uniqueness (multiplicity) within this class. We also study a special case with asymmetric bidders and show that concavity/convexity plays a similar role.

Suggested Citation

  • Guofu Tan & Okan Yilankaya, 2005. "Equilibria in Second Price Auctions with Participation Costs," IEPR Working Papers 05.7, Institute of Economic Policy Research (IEPR).
  • Handle: RePEc:scp:wpaper:05-7

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    References listed on IDEAS

    1. McAfee, R Preston & Quan, Daniel C & Vincent, Daniel R, 2002. "How to Set Minimum Acceptable Bids, with an Application to Real Estate Auctions," Journal of Industrial Economics, Wiley Blackwell, vol. 50(4), pages 391-416, December.
    2. Blume, Andreas & Heidhues, Paul, 2004. "All equilibria of the Vickrey auction," Journal of Economic Theory, Elsevier, vol. 114(1), pages 170-177, January.
    3. Steven A. Matthews, 1995. "A Technical Primer on Auction Theory I: Independent Private Values," Discussion Papers 1096, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Samuelson, William F., 1985. "Competitive bidding with entry costs," Economics Letters, Elsevier, vol. 17(1-2), pages 53-57.
    5. McAfee, R. Preston & McMillan, John, 1987. "Auctions with entry," Economics Letters, Elsevier, vol. 23(4), pages 343-347.
    6. 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.
    7. Stegeman, Mark, 1996. "Participation Costs and Efficient Auctions," Journal of Economic Theory, Elsevier, vol. 71(1), pages 228-259, October.
    8. King, Ian & Welling, Linda & Preston McAfee, R., 1992. "Investment decisions under first and second price auctions," Economics Letters, Elsevier, vol. 39(3), pages 289-293, July.
    9. Levin, Dan & Smith, James L, 1994. "Equilibrium in Auctions with Entry," American Economic Review, American Economic Association, vol. 84(3), pages 585-599, June.
    10. Tan, Guofu, 1992. "Entry and R & D in procurement contracting," Journal of Economic Theory, Elsevier, vol. 58(1), pages 41-60, October.
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    More about this item


    Second price auctions; participation cost; entry fee; multiplicity of equilibria;

    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
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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