Review of Economic Design

, Volume 13, Issue 1–2, pp 137–145 | Cite as

Non-existence of equilibrium in Vickrey, second-price, and English auctions

Original Paper

Abstract

A simple example shows that equilibria can fail to exist in second price (Vickrey) and English auctions when there are both common and private components to bidders’ valuations and private information is held on both dimensions. The example shows that equilibrium only exists in the extremes of pure private and pure common values, and that existence in standard models is not robust to a slight perturbation.

Keywords

Auction Equilibrium existence Nonexistence Vickrey auction Second-price auction English auction Multi-dimensional information 

JEL Classification

C62 C63 D44 D82 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Araujo ALI, de Castro, Moreira H (2004) Pure strategy equilibria of multidimensional and non-monotonic auctions, mimeo: IMPAGoogle Scholar
  2. Athey S (2001) Single crossing properties and the existence of pure strategy equilibria in games of incomplete information. Econometrica 69: 861–890CrossRefGoogle Scholar
  3. Jackson MO (1999) Non-existence of equilibrium in second price auctions with two dimensional types, mimeo: CaltechGoogle Scholar
  4. Jackson MO, Simon LK, Swinkels JM, Zame WR (2002) Communication and equilibrium in discontinuous games of incomplete information. Econometrica 70: 1711–1740CrossRefGoogle Scholar
  5. Jackson MO, Swinkels JM (2004) Existence of equilibria in single and double private value auctions. Econometrica 73: 93–139CrossRefGoogle Scholar
  6. Lebrun B (1999) First price auctions in the asymmetric N player case. Int Econ Rev 40: 125–142CrossRefGoogle Scholar
  7. Maskin E, Riley J (2000) Equilibrium in sealed high bid auctions. Rev Econ Stud 67: 439–452CrossRefGoogle Scholar
  8. McAdams D (2003) Isotone equilibrium in games of incomplete information. Econometrica 71: 1191–1214CrossRefGoogle Scholar
  9. Milgrom P (1981) Rational expectations, information acquisition, and competitive bidding. Econometrica 49: 921–944CrossRefGoogle Scholar
  10. Milgrom P, Weber R (1982) A theory of auctions and competitive bidding. Econometrica 50: 1089–1122CrossRefGoogle Scholar
  11. Pesendorfer W, Swinkels J (2000) Efficiency and information aggregation in auctions. Am Econ Rev 90: 499–525Google Scholar
  12. Reny PJ (1999) On the existence of pure and mixed strategy Nash equilibria in discontinuous games. Econometrica 67: 1029–1056CrossRefGoogle Scholar
  13. Reny PJ (2005) On the existence of monotone pure strategy equilibria in Bayesian games, mimeo: University of ChicagoGoogle Scholar
  14. Simon L, Zame W (1990) Discontinuous games and endogenous sharing rules. Econometrica 58: 861–872CrossRefGoogle Scholar
  15. Vickrey W (1961) Counterspeculation, auctions, and competitive sealed-tenders. J Finance 16: 8–37CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of EconomicsStanford UniversityStanfordUSA
  2. 2.External Faculty of the Santa Fe InstituteSanta FeUSA

Personalised recommendations