nep-des New Economics Papers
on Economic Design
Issue of 2021‒06‒28
seven papers chosen by
Guillaume Haeringer, Baruch College and Alex Teytelboym, University of Oxford

  1. Mechanism Design meets Priority Design: Redesigning the US Army’s Branching Process Through Market Design By Kyle Greenberg; Parag A. Pathak; Tayfun Sönmez
  2. Unique Stable Matchings By Gregory Z. Gutin; Philip R. Neary; Anders Yeo
  3. Preference revelation games and strict cores of multiple-type housing market problems By Bettina Klaus; Flip Klijn
  4. Preference revelation games and strict cores of multiple-type housing market problems By Di Feng; Bettina Klaus
  5. How Lotteries in School Choice Help to Level the Playing Field By Author-Name: Christian Basteck; Author-Name: Bettina Klaus; Dorothea Kuebler
  6. Cupid's Invisible Hand: Social Surplus and Identification in Matching Models By Alfred Galichon; Bernard Salani\'e
  7. Voting by Simultaneous Vetoes By Margarita Kirneva; Matias Nunez

  1. By: Kyle Greenberg (US Military Academy, West Point); Parag A. Pathak (MIT); Tayfun Sönmez (Boston College)
    Abstract: Army cadets obtain occupations through a centralized process. Three objectives – increasing retention, aligning talent, and enhancing trust – have guided reforms to this process since 2006. West Point’s mechanism for the Class of 2020 exacerbated challenges implementing Army policy aims. We formulate these desiderata as axioms and study their implications theoretically and with administrative data. We show that the Army’s objectives not only determine an allocation mechanism, but also a specific priority policy, a uniqueness result that integrates mechanism and priority design. These results led to a re-design of the mechanism, now adopted at both West Point and ROTC.
    Keywords: mechanism design, Army branch selection, priority design
    JEL: C78 D47 D63 D78
    Date: 2020–06–10
  2. By: Gregory Z. Gutin; Philip R. Neary; Anders Yeo
    Abstract: We provide necessary and sufficient conditions on the preferences of market participants for a unique stable matching in models of two-sided matching with non-transferable utility. We use the process of iterated deletion of unattractive alternatives (IDUA), a formalisation of the reduction procedure in Balinski and Ratier (1997), and we show that an instance of the matching problem possesses a unique stable matching if and only if IDUA collapses each participant preference list to a singleton. (This is in a sense the matching problem analog of a strategic game being dominance solvable.)
    Date: 2021–06
  3. By: Bettina Klaus; Flip Klijn
    Abstract: A classical school choice problem consists of a set of schools with priorities over students and a set of students with preferences over schools. Schools' priorities are often based on multiple criteria, e.g., merit-based test scores as well as minimal-access rights (siblings attending the school, students' proximity to the school, etc.). Traditionally, minimal-access rights are incorporated into priorities by always giving minimal-access students higher priority over non-minimal-access students. However, stability based on such adjusted priorities can be considered unfair because a minimal-access student may be admitted to a popular school while another student with higher merit-score but without minimal-access right is rejected, even though the former minimal-access student could easily attend another of her minimal-access schools. We therefore weaken stability to minimal-access stability: minimal-access rights only promote access to at most one minimal-access school. Apart from minimal-access stability, we also would want a school choice mechanism to satisfy strategy-proofness and minimal-access monotonicity, i.e., additional minimal-access rights for a student do not harm her. Our main result is that the student-proposing deferred acceptance mechanism is the only mechanism that satisfies minimal-access stability, strategy-proofness, and minimal-access monotonicity. Since this mechanism is in fact stable, our result can be interpreted as an impossibility result: fairer outcomes that are made possible by the weaker property of minimal-access stability are incompatible with strategy-proofness and minimal-access monotonicity.
    Keywords: school choice, priorities, minimal-access rights, justified envy, stability, deferred acceptance
    JEL: C78 D47 D63 D78
    Date: 2021–06
  4. By: Di Feng; Bettina Klaus
    Abstract: We consider multiple-type housing market problems as introduced by Moulin (1995) and study the relationship between strict strong Nash equilibria and the strict core (two solution concepts that are defined in terms of the absence of weak blocking coalitions). We prove that for lexicographically separable preferences, the set of all strict strong Nash equilibrium outcomes of each preference revelation game that is induced by a strictly core-stable mechanism is a subset of the strict core, but not vice versa, i.e., there are strict core allocations that cannot be implemented in strict strong Nash equilibrium (Theorem 1). This result is extended to a more general set of preference domains that satisfy strict core non-emptiness and a minimal preference domain richness assumption (Theorem 2).
    Keywords: multiple-type housing market problems, strict core, strict strong Nash equilibria
    JEL: C71 C72 C78
    Date: 2021–06
  5. By: Author-Name: Christian Basteck; Author-Name: Bettina Klaus; Dorothea Kuebler
    Abstract: School authorities in the UK and the US advocate the use of lotteries to desegregate schools. We study a school choice mechanism employed in Berlin where a lottery quota is embedded in the immediate acceptance (IA) mechanism, and compare it to the deferred acceptance mechanism (DA) with a lottery quota. In both mechanisms, some seats are allocated based on academic achievement (e.g., grades),while seats in the lottery quota are allocated randomly. We find that,in theory,a lottery quota strengthens truth-telling in DA by eliminating non-truth-telling equilibria. Furthermore, the equilibrium outcome is stable for DA with a lottery but not for IA with a lottery. These predictions are borne out in the experiment. Moreover, the lottery quota leads to more diverse school populations in the experiment, as predicted. Students with the lowest grades profit more from the introduction of the lottery under IA than under DA.
    Keywords: School choice, immediate acceptance mechanism, deferred acceptance, mechanism, lotteries, experiment, market design
    JEL: C78 C91 D47 D82 I24
    Date: 2021–06
  6. By: Alfred Galichon; Bernard Salani\'e
    Abstract: We investigate a model of one-to-one matching with transferable utility and general unobserved heterogeneity. Under a separability assumption that generalizes Choo and Siow (2006), we first show that the equilibrium matching maximizes a social gain function that trades off exploiting complementarities in observable characteristics and matching on unobserved characteristics. We use this result to derive simple closed-form formulae that identify the joint matching surplus and the equilibrium utilities of all participants, given any known distribution of unobserved heterogeneity. We provide efficient algorithms to compute the stable matching and to estimate parametric versions of the model. Finally, we revisit Choo and Siow's empirical application to illustrate the potential of our more general approach.
    Date: 2021–06
  7. By: Margarita Kirneva (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique, IP Paris - Institut Polytechnique de Paris, GENES - Groupe des Ecoles Nationales d'Economie et Statistique - Institut national de la statistique et des études économiques (INSEE)); Matias Nunez (CREST - Centre de Recherche en Economie et Statistique [Bruz] - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz], IP Paris - Institut Polytechnique de Paris, GENES - Groupe des Ecoles Nationales d'Economie et Statistique - Institut national de la statistique et des études économiques (INSEE))
    Abstract: We propose the first class of simultaneous voting mechanisms in which each Nash equilibrium is coalition-proof. These mechanisms hence prevent the coordination failures which arise when some (coalition of) voters could have induced an outcome that they all prefer to the equilibrium outcome had they agreed on a common strategy. In each of these mechanisms, some voter(s) has the right to veto a list of alternatives. For each specification of the veto rights, each of these mechanisms implements a Veto by random priority rule introduced by Moulin [1981]. We then discuss necessary conditions for arbitrary mechanisms to implement a Pareto efficient rule ensuring that each equilibrium is coalition-proof. We show that the presence of veto rights in the mechanism is unavoidable to achieve this demanding implementation notion.
    Keywords: Implementation,Voting,Vetoes,Coalition Formation,Efficiency
    Date: 2021–05–28

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