Add to ORKGWe study two-sided markets with a finite number of agents on each side, and with two-sided in-complete information. Agents are matched assortatively on the basis of costly signals. Asymmetries in signalling activity between the two sides of the market can be explained by asymmetries either 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 sig-nalling. Finally, we examine the limit model with a continuum of agents and point out differences and similarities to the finite version. Technically, the paper is based on the elegant theory about stochastic order relations among differences ...