Assortative matching through signals

In a model of sequential search with transferable utility, we allow heterogeneous agents to strategically choose a costless signal of their type. Search frictions are included as discounting and explicit search costs. Through signals, if only they are truthful, agents can avoid the inefficiencies of random search. Then the situation effectively approaches a setting without search frictions. We identify the condition under which signals are truthful and a unique separating equilibrium with perfect sorting arises despite frictions. We find that supermodularity of the match production function is a necessary and sufficient condition. This is a weaker condition than is needed for sorting in models without signals, which may explain why sorting is much more widespread in reality than existing models would suggest. Supermodularity functions here as both a sorting condition and a single-crossing property. The unique separating equilibrium in our model achieves nearly unconstrained efficiency despite frictions: agents successfully conclude their search after a single meeting, a stable matching results, and overall match output is maximised.