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


Klose, Bettina; Kovenock, Dan (2015). The all-pay auction with complete information and identity-dependent externalities. Economic Theory, 59(1):1-19.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Economics
Dewey Decimal Classification:330 Economics
Uncontrolled Keywords:All-pay auction, Identity-dependent externalities, Payoff nonequivalence, Contest, Political conflict, D44, D62, D72, C72
Language:English
Date:2015
Deposited On:06 Feb 2015 11:09
Last Modified:14 Feb 2018 08:57
Publisher:Springer
ISSN:0938-2259
Additional Information:The original publication is available at www.springerlink.com
OA Status:Closed
Publisher DOI:https://doi.org/10.1007/s00199-014-0848-5

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