The feedback effect in two-sided markets with bilateral investments

Agents in a finite two-sided market are matched assortatively, based on costly investments. Besides signaling privately known, complementary types, the investments also directly benefit the match partner. The bilateral external benefits induce a complex feedback cycle that amplifies the agents' signaling investments. Our main results quantify how the feedback effect depends on the numbers of competitors on both sides of the market. This yields detailed insights into the equilibria of two-sided matching contests with incomplete information, in particular for markets of small or intermediate size. It also allows us to shed some new light on the relationship between finite and continuum models of pre-match investment.