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...

There are at least two reasons why multiple prizes can be optimal in symmetric imperfectly discriminating contests. First, the introduction of multiple prizes reduces the standard deviation of contestants’ effort in asymmetric equilibria, when the majority of contestants actively participate...

The optimal contest architecture for symmetric imperfectly discriminating contests is shown to be generically the two-stage tournament (rather than the one-stage contest). In the first stage the contestants compete in several parallel divisions for the right to participate in the second stage....