All-pay matching contests

Abstract

We study two-sided matching contests with two sets, each of which includes two heterogeneous players with commonly known types. The players in each set compete in all-pay contests where they simultaneously send their costly e¤orts and then are assortatively matched. A player has a value function that depends on his type as well as his matched one. This model always has a corner equilibrium in which the players do not exert e¤orts and are randomly matched.However, we characterize the interior equilibrium and show that although players exert costly (wasted) e¤orts, this equilibrium might be either welfare superior or inferior to the corner equilibrium. We analyze the cross-e¤ects of the players' types on their expected payo¤s and also their e¤ect on the players'expected total e¤ort. We then show,that each of the players'types might have either a positive or a negative marginal e¤ect on their expected total e¤ort.