The all-pay auction with complete information

Abstract

This paper provides an exhaustive and explici[ description of the set of Nash equilibría in the n-player, first príce sealed bid, all pay auction under complete information.Both the cases of homogeneous and heterogeneous valuations are analyzed. For the common values case with more than two players we show there is a unique symmetric equilibrium and a continuum of asymmetric equilibria. All of the equilibria, however, are payoff and revenue equivalent. Wíth heterogeneous valua-Hence, while the equilibria are payoff equivalent, they are not revenue equivalent. The continua of asymmetric equilíbria were missed by both the theoretical literature, and the applied literature on e.g. rent seekíng and rent díssipation.

Continuous Time Contests with Private Information

“…As uncertainty vanishes, the distribution converges to the symmetric equilibrium distribution of an all-pay auction by Proposition 4. On the one hand, the model offers a microfoundation for the use of all-pay auctions to scrutinize environments containing little uncertainty; on the other hand, it gives an equilibrium selection criterion for the equilibria of the symmetric all-pay auction analyzed in Baye et al (1996). Furthermore, this result serves as a benchmark to discuss how our predictions differ from all-pay models if volatility is strictly positive.…”

Complementarity in contests

“…The contest success function in (i) di¤ers from typical applications of all-pay auctions (Hillman and Riley, 1989, Baye et. al., 1996, Che and Gale, 1998 only in that it is asymmetric and also it does not include an outcome that has a probability of 1/2 when the probability of guilt just equals .…”

“…We derive the functional form in (1) and its variations as an outcome of an audience's inference process when evidence production is deterministic and the contestants have a continuous probability distribution over the audience's priors. When the contestants know the audience's priors with certainty, we obtain the limiting case of the perfectly discriminating contest or the all-pay auction, whereby the contestant who puts more resources into the contest wins with certainty (see Hillman and Riley, 1989, Baye et. al., 1996, Che and Gale, 1998.…”

Extremism drives out moderation

“…2 In this sense we provide a bridge between models of conflict such as Linster (1993) and Esteban and Ray (1999) that utilize a lottery CSF and the growing literature on winner-pay auctions with identity-dependent externalities in which agents place bids, an auction CSF is employed, but generally all bids except for the winner's are refunded. Jehiel and Moldovanu(2006) review this literature and note that the endogeneity of valuations in winner-pay auctions is the main driving force behind many new, and interesting phenomena that arise even in complete 1 Linster (1993) argues that such a solution exists unless the contest is degenerate in the sense that players are indifferent to the outcome.…”