All-pay matching contests

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 efforts 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 efforts and are randomly matched. We characterize the interior equilibrium and show that although players exert costly (wasted) efforts, this equilibrium might be welfare superior to the corner equilibrium. We analyze the cross effects of the players’ types on the expected payoffs of the other players as well as on their effect on the players’ expected total effort, and demonstrate the complexity of these cross effects.