The pre-marital investment game

Two sides of a finite marriage market engage in costly investment and are then matched assortatively. The purpose of the investment is solely to improve the quality of the match that the trader can attain in the second stage. The paper studies the limits of equilibrium of these finite matching games as the number of traders gets large. It is shown that mixed Nash equilibria in the finite games converge to degenerate pure strategy equilibria in the limit in which both sides of the market invest too much.