David Delacrétaz
Ph.D. Candidate – Department of Economics – The University of Melbourne

Job Market Paper

Stability in Matching Markets with Sizes

(Earlier versions of this paper circulated under the title “Matching with Quantity”.)

Abstract: Matching markets such as day care, tuition exchange, couples problems and refugee resettlement involve agents of different sizes. The size of an agent is the amount of capacity that he uses. In matching markets where all agents have the same size, there exists an agent-optimal stable matching. This structure disappears when agents have different sizes: the set of stable matchings may not contain an agent-optimal element and may even be empty. In this paper, we study a matching market where the size of an agent is either one or two. We propose a novel and constructive algorithm to find an agent-undominated stable matching whenever one exists. We introduce a novel relaxation of stability: size-stability. Size-stable matchings are non-wasteful but allow size-two agents to envy multiple size-one agents. We show that the set of size-stable matchings is nonempty. We adapt our algorithm to find a size-stable matching that is undominated from the point of view of size-two agents, thus compensating them for envying size-one agents. In the process, we outline a new trade-off between eliminating waste and bounding envy: at any non-wasteful matching, an agent may envy arbitrarily many other agents.

Working Papers

Two-Sided Allocation Problems, Matching with Transfers, and the Impossibility of Ex Post Efficiency 
(with Simon Loertscher, Leslie Marx, and Tom Wilkening)

Revise and ResubmitJournal of Economic Theory

Abstract: Calling a two-sided allocation problem a matching problem if it can be represented as an assignment game, we show that ex post efficient trade is impossible for all matching problems. Generalizing Shapley’s (1962) theorem, we show that a necessary and sufficient condition for a two-sided allocation problem to be a matching problem is that each agent can be decomposed into constituents with unit capacities. The family of rank-dependent discounts payoff functions, which we introduce, nests many important specifications, is sufficient for decomposability and, therefore, for impossibility of ex post efficient trade.

Refugee Resettlement (with Scott Duke Kominers and Alexander Teytelboym)

Media coverage: BloombergNews Deeply
Application: Refugees’ Say

Abstract: Over 100,000 refugees are permanently resettled from refugee camps to hosting countries every year. Nevertheless, refugee resettlement processes in most countries are ad hoc accounting for neither the priorities of hosting communities nor the preferences of refugees themselves. Building on models from two-sided matching theory, we introduce a new framework for matching with multidimensional constraints that models refugee families’ needs for multiple units of different services, as well as the service capacities of local areas. We propose several refugee resettlement mechanisms that can be used by hosting countries under various institutional and informational constraints. Our mechanisms can improve match efficiency, incentivize refugees to report where they would like to settle, and respect priorities of local areas thereby encouraging them to accept more refugees overall. Beyond the refugee resettlement context, our model has applications ranging from the allocation of daycare slots to the incorporation of complex diversity constraints in public school assignment.

Work in Progress

Uncontrolled Immigration and Refugee Matching (with Ellen Muir)

Efficient and Essentially Stable Assignments (with Andrew Kloosterman and Peter Troyan)
(A draft of this paper already exists. I am collaborating on the next version.)