Advances in Matching Theory

Paper Session

Sunday, Jan. 8, 2017 1:00 PM – 3:00 PM

Hyatt Regency Chicago, Dusable
Hosted By: Econometric Society
  • Chair: Guillaume Haeringer, Baruch College

Timely Matching

Guillaume Haeringer
,
Baruch College
Vincent Iehle
,
Paris Dauphine University

Abstract

A common practice for centralized clearinghouses is to compute, once and for all, the final allocation of students at a given date. Sometimes, however, a clearinghouse may proceed sequentially by computing allocations at earlier dates, leaving the option to participants to finalize their match before the final date. We characterize the conditions under which such multi-period matching mechanisms produce stable matchings (with a stability concept adapted to this environment). Matching mechanisms with multiple periods can be modeled as a one-period mechanism by taking account of additional source of heterogeneity among participants like scheduling constraints (ignored so far in the matching literature of matching), by allowing them to express preferences over potential matches and the date at which they are matched. These unconventional clearinghouses partially succeed in maintaining desirable properties of two-sided matchings. We use our results to evaluate the French college admission mechanism, where students can finalize their matches up to two months ahead the final date.

Welfare and Entropy in Many-to-Many Matching

Marcin Peski
,
University of Toronto

Abstract

We propose a strategic model of many-to-many matching with nontransferable<br /><br />
utility. In the model, individuals dynamically search for match partners. The utility generalizes Dagsvik (2000) and consists of two terms: a deterministic part that depends only on the types of matched individuals and a random part that is the sum of the idiosyncratic shocks for each partner. The main result characterizes the stationary equilibrium distribution over the types of matched partners. We show that each such distribution is a critical point of a functional that is the sum of two terms: The first term can be interpreted as the average welfare and the second as the average entropy of the allocation. All second- and higher (discrete versions of) derivatives of the utility, including the payoff externalities, can be identified from the equilibrium distribution.

Optimal Dynamic Matching

SangMok Lee
,
University of Pennsylvania
Mariagiovanna Baccara
,
University of Washington-St Louis
Leeat Yariv
,
California Institute of Technology

Abstract

We study a dynamic matching environment where individuals arrive sequentially. There is a tradeoff between waiting for a thicker market, allowing for higher quality matches and minimizing agentsíwaiting costs. The optimal mechanism cumulates a stock of incongruent pairs up to a threshold and matches all others in an assortative fashion instantaneously. In decentralized settings, a similar protocol ensues in equilibrium, but expected queues are inefficiently long. We quantify the welfare gain from centralization, which can be substantial, even for low waiting costs. We also evaluate welfare improvements generated by transfer schemes and by matching individuals in fixed time intervals.

The Design of Teacher Assignment: Theory and Evidence

Camille Terrier
,
Paris School of Economics and London School of Economics
Julien Combe
,
Paris School of Economics
Olivier Tercieux
,
Paris School of Economics

Abstract

To assign teachers to schools, a modifi ed version of the well-known deferred acceptance mechanism has been proposed in the literature and is used in practice. We show that this mechanism fails to be fair and efficient for both teachers and schools. We identify the unique strategy-proof mechanism that cannot be improved upon in terms of both efficiency and fairness. We show that this mechanism performs much better by adopting a large market approach and by using a rich dataset on teachers' applications for transfers in France. For instance, the number of teachers moving from their positions more than doubles under our mechanism.
JEL Classifications
  • C0 - General