The Theory of Assortative Matching Based on Costly Signals

We study two-sided markets with a finite numbers of agents on each side, and with two-sided incomplete information. Agents are matched assortatively on the basis of costly signals. We rst analyze how signaling and welfare on each side of the market change when we vary the number of agents. Next we show that asymmetries in signaling activity between the two sides of the market can be explained either by asymmetries in size or in heterogeneity. Our main results identify general conditions under which the potential increase in expected output due to assortative matching (relative to random matching) is offset by the costs of signaling. Finally, we look at a version with a continuum of agents, and we establish the di¤erences and similarities to the finite version. In particular, we characterize instances where the insights obtained for the continuum version apply also to small markets, and illustrate situations where they do not. Technically, the paper is based on the elegant theory about stochastic order relations among di¤erences of order statistics, pioneered by R. Barlow and F. Proschan (1966, 1975) in the framework of reliability theory