“You’re just my type!” Matching and payoffs when like attracts like

I analyse a marriage market with transferable utility when the output of two matched agents is a decreasing function of the difference in their types i.e. like attracts like. The pattern of sorting and payoffs exhibit many features not found in the standard model, where more is always better. Full positive sorting occurs not only if the output function is concave (equivalent to supermodularity) but also if the distribution of types is the same on each side of the market, regardless of the technology. Convexity of the output function is not in general equivalent to submodularity and negative sorting occurs only if there is no overlap in the two type distributions; otherwise there is a mix of perfect matching and negative sorting. For both sides of the market, payoffs as a function of type tend to display a wavelike pattern and are only weakly connected to the quality of the match an agent is in. At types where one payoffs function is increasing, the other is decreasing. With convexity, we have maximum possible matching of like with exactly like, so for agents on the long side of the market their optimal choice of partner is not unique. Even though like is attracted to like, having a type close to the mean type on the other side does not always imply a high payoffs, and when the marriage market is embedded in a wider economy providing outside options such agents may well remain single.