DP14610 Two-Stage Matching Contests
We study two-sided matching contests with two sets of agents, each of which includes n heterogeneous agents with commonly known types. In the first stage, the agents simultaneously send their costly efforts and then the order of choosing a partner from the other set is determined according to the Tullock contest success function. In the second stage, each agent chooses a partner from the other set, and an agent has a positive revenue if there is a matching in which he chooses a partner from the other set and this partner also chooses him. We analyze the agents' equilibrium efforts in the first stage as well as their choices of partners in the second stage, and demonstrate that if the agents' values, which are functions of the types of the agents who are matched, are either multiplicative or additive, their efforts are not necessarily monotonically increasing in their types.