The Stability of Hedonic Coalition Structures

The design of the New York City (NYC) High School match involved tradeoffs among efficiency, stability and strategy-proofness that raise new theoretical questions. We analyze a model with indifferences--ties--in school preferences. Simulations with field data and the theory favor breaking indifferences the same way at every school --single tie breaking-- in a student-proposing deferred acceptance mechanism. Any inefficiency associated with a realized tie breaking cannot be removed without harming student incentives. Finally, we empirically document the extent of potential efficiency loss associated with strategy-proofness and stability, and direct attention to some open questions.

Strategy-Proofness Versus Efficiency in Matching with Indifferences: Redesigning the New York City High School Match

The deferred acceptance algorithm proposed by Gale and Shapley (1962) has had a profound influence on market design, both directly, by being adapted into practical matching mechanisms, and, indirectly, by raising new theoretical questions. Deferred acceptance algorithms are at the basis of a number of labor market clearinghouses around the world, and have recently been implemented in school choice systems in Boston and New York City. In addition, the study of markets that have failed in ways that can be fixed with centralized mechanisms has led to a deeper understanding of some of the tasks a marketplace needs to accomplish to perform well. In particular, marketplaces work well when they provide thickness to the market, help it deal with the congestion that thickness can bring, and make it safe for participants to act effectively on their preferences. Centralized clearinghouses organized around the deferred acceptance algorithm can have these properties, and this has sometimes allowed failed markets to be reorganized.

Deferred Acceptance Algorithms: History, Theory, Practice, and Open Questions

The paper analyzes incentives and stability in two-sided matching markets when the number of participants is large and the length of the preference list is finite. Building on and extending Immorlica and Mahdian (2005), we first investigate the scope for manipulation in a many-to-one market. When preference lists are drawn from an arbitrary distribution for one side of the market and under a mild independence assumption on the distribution for the other side, we establish that the fraction of participants who can profitably misrepresent their preferences via truncation is small. Moreover, the scope of manipulations via capacities and pre-arranged matches approaches zero as the size of the market becomes large. With an additional bounded distribution assumption, truthful reporting is an approximate equilibrium, implying efficiency of the resulting matching.

/pdf/incentives-and-stability-in-large-two-sided-matching-markets-3rmt8e9j9m.pdf

Incentives and Stability in Large Two-Sided Matching Markets

The design of the New York City (NYC) high school match involved trade-offs among efficiency, stability, and strategy-proofness that raise new theoretical questions. We analyze a model with indifferences—ties—in school prefer - ences. Simulations with field data and the theory favor breaking indifferences the same way at every school—single tiebreaking—in a student-proposing deferred acceptance mechanism. Any inefficiency associated with a realized tiebreaking cannot be removed without harming student incentives. Finally, we empirically document the extent of potential efficiency loss associated with strategy-proofness and stability, and direct attention to some open questions. (JEL C78, D82, I21)

/pdf/strategy-proofness-versus-efficiency-in-matching-with-2dqk9m28jp.pdf

Strategy-Proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match

https://ddd.uab.cat/pub/worpap/2007/hdl_2072_3645/67106.pdf

Constrained school choice

The literature on school choice assumes that families can submit a preference list over all the schools they want to be assigned to. However, in many real-life instances families are only allowed to submit a list containing a limited number of schools. Subjects' incentives are drastically affected, as more individuals manipulate their preferentes. Including a safety school in the constrained list explains most manipulations. Competitiveness across schools plays an important role. Constraining choices increases segregation and affects the stability and efficiency of the final allocation. Remarkably, the constraint reduces significantly the proportion of subjects playing a dominated strategy.

/pdf/constrained-school-choice-an-experimental-study-ycnoj2pgus.pdf

Constrained School Choice: An Experimental Study

31 pages, 18 tables.-- JEL classification: C72, C78, D78, I20.-- Trabajo publicado como articulo en American Economic Review 100(4): 1860-1874 (2010).-- http://dx.doi.org/10.1257/aer.100.4.1860

/pdf/constrained-school-choice-an-experimental-study-22pnvzpk83.pdf

Constrained school choice: an experimental study

We provide in this paper two properties that are both necessary and sufficient to characterize the domain of single-peaked preference profiles. This characterization allows for a definition of single-peaked preference profiles without using an ad hoc underlying order of the alternatives and also sheds light on the structure of single-peaked profiles. Considering the larger domain of value-restricted preference profiles (Sen, Econometrica 34:491–499, 1966) we also provide necessary and sufficient conditions for a preference profile to be single-caved or group-separable. Our results show that for single-peaked, single-caved and group-separable profiles it is sufficient to restrict to profiles containing of either three individuals and three alternatives or two individuals and four alternatives.

A characterization of the single-peaked domain

https://www.beta-umr7522.fr/productions/publications/1999/9910.pdf

Guillaume Haeringer

Papers

Constrained school choice

Constrained School Choice: An Experimental Study

Constrained school choice: an experimental study

A characterization of the single-peaked domain

A new weight scheme for the Shapley value