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Matching and market design in the latest issue of Theoretical Economics
Theoretical Economics, Volume 14, Number 4 (November 2019) has several articles on matching and market design
Common enrollment in school choice
Mehmet Ekmekci, M. Bumin Yenmez
Abstract: Increasingly, more school districts across the US are using centralized admissions for charter, magnet, and neighborhood schools in a common enrollment system. We first show that, across all school-participation patterns, full participation in the common (or unified) enrollment system leads to the most preferred outcome for students. Second, we show that, in general, participation by all schools may not be achievable because schools have incentives to stay out. This may explain why some districts have not managed to attain full participation. We also consider some specific settings where full participation can be achieved and propose two schemes that can be used by policymakers to achieve full participation in general settings.
School choice under partial fairness
Umut Dur, A. Arda Gitmez, Özgür Yılmaz
Abstract: We generalize the school choice problem by defining a notion of allowable priority violations. In this setting, a weak axiom of stability (partial stability) allows only certain priority violations. We introduce a class of algorithms called the Student Exchange under Partial Fairness (SEPF). Each member of this class gives a partially stable matching that is not Pareto dominated by another partially stable matching (i.e. constrained efficient in the class of partially stable matchings). Moreover, any constrained efficient matching that Pareto improves upon a partially stable matching can be obtained via an algorithm within the SEPF class. We characterize the unique algorithm in the SEPF class satisfying a desirable incentive property. The extension of the model to an environment with weak priorities enables us to provide a characterization result which proves the counterpart of the main result in Erdil and Ergin (2008).
Full substitutability
John William Hatfield, Scott Duke Kominers, Alexandru Nichifor, Michael Ostrovsky, Alexander Westkamp
Abstract: Various forms of substitutability are essential for establishing the existence of equilibria and other useful properties in diverse settings such as matching, auctions, and exchange economies with indivisible goods. We extend earlier models' definitions of substitutability to settings in which each agent can be both a buyer in some transactions and a seller in others, and show that all these definitions are equivalent. We then introduce a new class of substitutable preferences that allows us to model intermediaries with production capacity. We also prove that substitutability is preserved under economically important transformations such as trade endowments, mergers, and limited liability.
Common enrollment in school choice
Mehmet Ekmekci, M. Bumin Yenmez
Abstract: Increasingly, more school districts across the US are using centralized admissions for charter, magnet, and neighborhood schools in a common enrollment system. We first show that, across all school-participation patterns, full participation in the common (or unified) enrollment system leads to the most preferred outcome for students. Second, we show that, in general, participation by all schools may not be achievable because schools have incentives to stay out. This may explain why some districts have not managed to attain full participation. We also consider some specific settings where full participation can be achieved and propose two schemes that can be used by policymakers to achieve full participation in general settings.
School choice under partial fairness
Umut Dur, A. Arda Gitmez, Özgür Yılmaz
Abstract: We generalize the school choice problem by defining a notion of allowable priority violations. In this setting, a weak axiom of stability (partial stability) allows only certain priority violations. We introduce a class of algorithms called the Student Exchange under Partial Fairness (SEPF). Each member of this class gives a partially stable matching that is not Pareto dominated by another partially stable matching (i.e. constrained efficient in the class of partially stable matchings). Moreover, any constrained efficient matching that Pareto improves upon a partially stable matching can be obtained via an algorithm within the SEPF class. We characterize the unique algorithm in the SEPF class satisfying a desirable incentive property. The extension of the model to an environment with weak priorities enables us to provide a characterization result which proves the counterpart of the main result in Erdil and Ergin (2008).
Full substitutability
John William Hatfield, Scott Duke Kominers, Alexandru Nichifor, Michael Ostrovsky, Alexander Westkamp
Abstract: Various forms of substitutability are essential for establishing the existence of equilibria and other useful properties in diverse settings such as matching, auctions, and exchange economies with indivisible goods. We extend earlier models' definitions of substitutability to settings in which each agent can be both a buyer in some transactions and a seller in others, and show that all these definitions are equivalent. We then introduce a new class of substitutable preferences that allows us to model intermediaries with production capacity. We also prove that substitutability is preserved under economically important transformations such as trade endowments, mergers, and limited liability.
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