All-pay contests with performance spillovers

This paper generalizes the results of Siegel (2009, 2010) to accommodate performance spillovers, with which a player's performance in a contest may affect the performance cost of another player. More precisely, we show that, if for any player, the spillovers from other players' performance enter his cost in an additively separable form, then an all-pay contest has a unique Nash equilibrium. Moreover, we construct the equilibrium payoffs and strategies. Both the equilibrium uniqueness and construction are generalized to multiplicatively separable spillovers in a two-player contest.