The multiplier effect in two-sided markets with bilateral investments

Agents in a finite two-sided market make costly investments and are then matched assortatively based on these investments. Besides signaling complementary types, investments also generate benefits for partners. We shed light on quantitative properties of the equilibrium investment behavior. The bilateral external benefits induce an investment multiplier effect. This multiplier effect depends in a complex way on agents' uncertainty about their rank within their own market side and on their uncertainty about the types and investments of potential partners. We study how the multiplier effect depends on market size and how it interacts with other important factors such as the costs of investment and the signaling incentives induced by competition for more desirable partners. We use our results to characterize equilibrium utilities in large markets. For small markets, our results lead to bounds on the hold-up problem.