Journal of Economic Behavior & Organization, January 2018, 145: 114-140.
Abstract. We study the stability on many-to-one matching markets in a dynamic framework with the following features: matching is irreversible, participants -exogenously- join market over time, and each agent on one side is restricted by a quota, and agents are perfectly patient. A form of strategic behavior in such markets emerges: the side with many slots can manipulate the subsequent matching market in their favor via earlier matchings. In such a setting, a natural question arises: can we analyze a dynamic many-to-one matching market as if it were either a static many-to-one or a dynamic one-to-one market? First, we provide sufficient conditions under which the answer is yes. Second, we show that if these conditions are not met, then the early matchings are inferior compared to the subsequent matchings. Lastly, we extend the model to allow agents on one side to endogenously decide when to join the market. Using this extension we provide a rationale for little unraveling observed in the US medical residency matching market compared to the US college admissions system.
Abstract. We consider a monopolist who is facing loss-averse buyers over two periods, with an uncertain demand in the second period. Monopolist cannot commit today to a future price, and posts the price for tomorrow only after the demand realization. We incorporate best-price provision policy into the monopolist’s problem, in the form of a most-favored-customer (MFC) clause, which is an own-price match guarantee. We solve for the dynamic pricing problem of such a monopolist under loss aversion both with and without an MFC clause. We show that for a wide range of discount factors, the monopolist optimally adopts MFC if and only if the buyers are loss-averse. Also, the result holds for any discount factor when buyers are sufficiently loss-averse. We also make inferences on the residual demand, which reflects the set of buyers who choose to wait for tomorrow to purchase.
Abstract. This paper studies the menu of licenses designed by the child welfare agency to screen foster parents. We develop a two-sided matching model with heterogeneous agents, search frictions, private information, and a designer who coordinates match formation through a menu of contracts. We focus on incentive-compatible contracts, examine optimal transfers, and analyze sorting patterns that arise in equilibrium. We establish three main results: (i) foster parents in different licenses will never care for the same group of foster children, (ii) complementarities do not ensure that Positive Assortative Matching (PAM) will arise in equilibrium, thus we provide additional condition that guarantees PAM, and (iii) the equilibrium transfer scheme is not unique and does not affect the unique equilibrium sorting pattern. Moreover, our results suggest that an optimal menu of licenses must not only account for the child’s attribute (as it is in practice), but also for other characteristics of the market such as parents’ types, supply of parents, and supply of children.
Dynamic Matching: Shall we commit to not competing? (draft coming soon)
Abstract. Commitment exists in various contexts and forms in economics. It appears in a particular way in dynamic many-to-one matching markets when matchings are irreversible: Institutions may commit to matching with specific agents early on to affect the subsequent matching market in their favor. This paper introduces a suitable notion of dynamic group stability and shows that institutions can benefit from committing to match worse early on. It is because such a commitment lowers the competition for better agents in the subsequent market. Such equilibria rationalize empirical evidence on early-regular college admission in the US, as well as the job market for Finance Ph.D. candidates.