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The All-Pay Auction with Complete Information and Identity-Dependent Externalities

  • Bettina Klose

    (Department of Economics, University of Zurich)

  • Dan Kovenock

    (Economic Science Institute, Chapman University)

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 (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 winner-pay auction 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 in the winner-pay auction and vice versa.

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Paper provided by Chapman University, Economic Science Institute in its series Working Papers with number 13-10.

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Length: 18 pages
Date of creation: 2013
Date of revision:
Handle: RePEc:chu:wpaper:13-10
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