"Assortative Matching with On-the-Match Search" 
with Hector Chade

Abstract. We analyze two-sided matching markets with heterogeneous agents who search for partners while unmatched or matched. We contribute by finding conditions on the match payoff function such that every equilibrium exhibits Positive Assortative Matching (PAM) when on-the match search is allowed, and utility is strictly non-transferable. Since match-status and match-partners may vary over time, we say that an equilibrium exhibits PAM if the conditional cumulative distribution function over matches is increasing in the agents' attributes. The reversibility on matches adds a trade-off absent in models where matches are irreversible: agents not only care about the payoff received from the match but also the likelihood that the partner leaves, and they become unmatched. In our environment, the probability that a match disrupts is an endogenous object determined in equilibrium and can potentially vary across agents' attributes. We find that, in equilibrium, partners who produce higher payoffs are not always preferred since there is a higher probability that they leave to form a new match. Preliminary results suggest that, if the match payoff function is strictly increasing in the partner's attribute, then the equilibrium sorting exhibits PAM. Currently, we are generalizing the analysis in several directions, including allowing for transfers.