Pre-Match Investment Competition with Bounded Transfers

This paper studies pre-match investment competition with upper and lower bounds on feasible transfers to sellers in a general signaling environment, where the types of buyers and sellers are private information and the surplus may depend on both types and investments. Bounded transfers create methodological challenges -- e.g., externalities in the bottom match, limits of a separate investment reward (or market utility) schedule for each side -- that would be present even in a large market. To overcome such challenges, this paper proposes a notion of equilibrium that incorporates strategic behavior of a continuum of agents. Given our notion of equilibrium with bounded transfers, our model explains remarkably well why sellers and buyers in the bottom tail of the match distribution are stuck in a vicious cycle of a rat race, and how stars who stand out from the rest endogenously arise through pre-match investment competition.