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Economic Theory

, Volume 59, Issue 1, pp 1–19 | Cite as

The all-pay auction with complete information and identity-dependent externalities

  • Bettina Klose
  • Dan Kovenock
Research Article

Abstract

We derive a necessary and sufficient condition for the existence of equilibria with only two active players in the all-pay auction with complete information and identity-dependent externalities. This condition shows that the generic equilibrium of the standard all-pay auction is robust to the introduction of “small” identity-dependent externalities. In general, however, the presence of identity-dependent externalities invalidates well-established qualitative results concerning the set of equilibria of the first-price all-pay auction with complete information. With identity-dependent externalities, equilibria are generally not payoff equivalent, and identical players may earn different payoffs in equilibrium. These observations show that Siegel’s (Econometrica 77(1), 71–92, 2009) results characterizing the set of equilibrium payoffs in all-pay contests, including the all-pay auction as a special case, do not extend to environments with identity-dependent externalities. We further compare the all-pay auction with identity-dependent externalities to the first-price winner-pay auction with identity-dependent externalities. We demonstrate that the equilibrium payoffs of the all-pay auction and the “undominated strategy equilibrium” payoffs of the winner-pay auction (Funk in Int J Game Theory 25(1), 51–64, 1996) cannot be ranked unambiguously in the presence of identity-dependent externalities by providing examples of environments where equilibrium payoffs in the all-pay auction dominate those of the undominated strategy equilibria in the winner-pay auction and vice versa.

Keywords

All-pay auction Identity-dependent externalities  Payoff nonequivalence Contest Political conflict 

JEL Classification

D44 D62 D72 C72 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.University of ZurichZurichSwitzerland
  2. 2.Chapman UniversityOrangeUSA

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