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. A main goal is to identify conditions under which the potential increase in expected output due to assortative matching (relative to random matching) is completely offset by the costs of signalling. We also study how the signalling activity and welfare on each side of the market change when we vary the number of agents and the distribution of their attributes, thereby displaying effects that are particular to small markets. Finally, we look at the continuous version of our two-sided market model and establish the connections to the finite version. Technically, the paper is based on the very elegant theory about stochastic ordering of (normalized) spacings and other linear combinations of order statistics from distributions with monotone failure rates, pioneered by R. Barlow and F. Proschan (1966, 1975) in the framework of reliability theory.