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 agents in each set compete in all-pay contests where they simultaneously send their costly efforts, and then are either assortatively or disassortatively matched. We characterize the players' equilibrium efforts for a general value function that assigns values for both agents who are matched as a function of their types. We then analyze the cross-effects of the players' types on their expected payoffs as well as on their expected total effort. We show that although each player's value function increases (decreases) in the types of the players in the other set, his expected payoff does not necessarily increase (decrease) in these types. In addition, depending on the value function, each player's type might have either a positive or a negative marginal effect on the players' expected total effort.