Theory and Decision

, Volume 71, Issue 2, pp 269–295 | Cite as

Endogenous entry in lowest-unique sealed-bid auctions

  • Harold Houba
  • Dinard van der Laan
  • Dirk Veldhuizen
Open Access


Lowest-unique sealed-bid auctions are auctions with endogenous participation, costly bids, and the lowest bid among all unique bids wins. Properties of symmetric NEs are studied. The symmetric NE with the lowest expected gains is the maximin outcome under symmetric strategies, and it is the solution to a mathematical program. Comparative statics for the number of bidders, the value of the item and the bidding cost are derived. The two bidders’ auction is equivalent to the Hawk–Dove game. Simulations of replicator dynamics provide numerical evidence that the symmetric NE with the lowest expected gains is also asymptotically stable.


Sealed-bid auction Evolutionary stability Endogenous entry Maximin 

JEL Classification

D44 C72 C73 C61 L83 



We are grateful to Quan Wen and Gerard van der Laan for valuable suggestions.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


  1. Becker J., Damianov D. (2006) On the existence of symmetric mixed strategy equilibria. Economics Letters 90: 84–87CrossRefGoogle Scholar
  2. Betounes D. (2001) Differential equations: Theory and applications with Maple. Springer, BerlinGoogle Scholar
  3. Brooke, A., Kendrick, D., Meeraus, A., & Raman, R. (1998). Gams: A users guide. Available at the GAMS Development Corporation web site at
  4. Bukowski M., Miekisz J. (2004) Evolutionary and asymptotic stability in symmetric multi-player games. International Journal of Game Theory 33: 41–54CrossRefGoogle Scholar
  5. Crouzeix J.-P., Lindberg P. (1986) Additively decomposed quasiconvex functions. Mathematical Programming 35: 42–57CrossRefGoogle Scholar
  6. Eichberger J., Vinogradov D. (2008) Least unmatched price auctions. University of Heidelberg, Mimeo, HeidelbergGoogle Scholar
  7. Houba, H., van der Laan, D., & Veldhuizen, D. (2008). The lowest-unique sealed-bid auction. TI Discussion Paper 08-049, Tinbergen Institute, Amsterdam/Rotterdam. Available at
  8. Krishna V. (2002) Auction theory. Academic Press, San DiegoGoogle Scholar
  9. McKelvey R., Palfrey T. (1995) Quantal response equilibria for normal form games. Games and Economic Behavior 10: 6–38CrossRefGoogle Scholar
  10. McKelvey, R., Richard, D., McLennan, A., & Turocy, T. (2006). Gambit: Software tools for game theory, version 0.2006.01.20.
  11. Myerson R. (1998) Population uncertainty and poisson games. International Journal of Game Theory 27: 375–392CrossRefGoogle Scholar
  12. Myerson R. (2000) Large poisson games. Journal of Economic Theory 94: 7–45CrossRefGoogle Scholar
  13. Östling, R., Wang, J., Chou, E., & Camerer C. (2007). Field and lab convergence in poisson lupi games. SSE/EFI working paper series in Economics and Finance 671.Google Scholar
  14. Rapoport, A., Otsubo H., Kim B., & Stein W. (2007). Unique bid auctions: Equilibrium solutions and experimental evidence. Discussion Paper, University of Arizona.Google Scholar
  15. Raviv Y., Virag G. (2008) Gambling by auctions. International Journal of Industrial Organization 27: 369–378CrossRefGoogle Scholar
  16. Weibull J. (1995) Evolutionary game theory. MIT Press, CambridgeGoogle Scholar

Copyright information

© The Author(s) 2010

Authors and Affiliations

  • Harold Houba
    • 1
  • Dinard van der Laan
    • 1
  • Dirk Veldhuizen
    • 2
  1. 1.Department of EconometricsVU University Amsterdam, Tinbergen InstituteAmsterdamNetherlands
  2. 2.SNS Reaal, Group Risk ManagementUtrechtThe Netherlands

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