College admissions with stable score-limits

A common feature of the Hungarian, Irish, Spanish and Turkish higher education admission systems is that the students apply for programmes and they are ranked according to their scores. Students who apply for a programme with the same score are in a tie. Ties are broken by lottery in Ireland, by objective factors in Turkey (such as date of birth) and other precisely defined rules in Spain. In Hungary, however, an equal treatment policy is used, students applying for a programme with the same score are all accepted or rejected together. In such a situation there is only one question to decide, whether or not to admit the last group of applicants with the same score who are at the boundary of the quota. Both concepts can be described in terms of stable score-limits. The strict rejection of the last group with whom a quota would be violated corresponds to the concept of H-stable (i.e. higher-stable) score-limits that is currently used in Hungary. We call the other solutions based on the less strict admission policy as L-stable (i.e. lower-stable) score-limits. We show that the natural extensions of the Gale-Shapley algorithms produce stable score-limits, moreover, the applicant-oriented versions result in the lowest score-limits (thus optimal for students) and the college-oriented versions result in the highest score-limits with regard to each concept. When comparing the applicant-optimal H-stable and L-stable score-limits we prove that the former limits are always higher for every college. Furthermore, these two solutions provide upper and lower bounds for any solution arising from a tie-breaking strategy. Finally we show that both the H-stable and the L-stable applicant-proposing scorelimit algorithms are manipulable

Coalitions and Cliques in the School Choice Problem

The school choice mechanism design problem focuses on assignment mechanisms matching students to public schools in a given school district. The well-known Gale Shapley Student Optimal Stable Matching Mechanism (SOSM) is the most efficient stable mechanism proposed so far as a solution to this problem. However its inefficiency is well-documented, and recently the Efficiency Adjusted Deferred Acceptance Mechanism (EADAM) was proposed as a remedy for this weakness. In this note we describe two related adjustments to SOSM with the intention to address the same inefficiency issue. In one we create possibly artificial coalitions among students where some students modify their preference profiles in order to improve the outcome for some other students. Our second approach involves trading cliques among students where those involved improve their assignments by waiving some of their priorities. The coalition method yields the EADAM outcome among other Pareto dominations of the SOSM outcome, while the clique method yields all possible Pareto optimal Pareto dominations of SOSM. The clique method furthermore incorporates a natural solution to the problem of breaking possible ties within preference and priority profiles. We discuss the practical implications and limitations of our approach in the final section of the article

College admissions and the role of information : an experimental study

We analyze two well-known matching mechanisms—the Gale-Shapley, and the Top Trading Cycles (TTC) mechanisms—in the experimental lab in three different informational settings, and study the role of information in individual decision making. Our results suggest that—in line with the theory—in the college admissions model the Gale-Shapley mechanism outperforms the TTC mechanisms in terms of efficiency and stability, and it is as successful as the TTC mechanism regarding the proportion of truthful preference revelation. In addition, we find that information has an important effect on truthful behavior and stability. Nevertheless, regarding efficiency, the Gale-Shapley mechanism is less sensitive to the amount of information participants hold

An Experimental Investigation of Preference Misrepresentation in the Residency Match

The development and deployment of matching procedures that incentivize truthful preference reporting is considered one of the major successes of market design research. In this study, we test the degree to which these procedures succeed in eliminating preference misrepresentation. We administered an online experiment to 1,714 medical students immediately after their participation in the medical residency match--a leading field application of strategy-proof market design. When placed in an analogous, incentivized matching task, we find that 23% of participants misrepresent their preferences. We explore the factors that predict preference misrepresentation, including cognitive ability, strategic positioning, overconfidence, expectations, advice, and trust. We discuss the implications of this behavior for the design of allocation mechanisms and the social welfare in markets that use them

Incomplete Information and Small Cores in Matching Markets

We study Bayesian Nash equilibria of stable mechanisms in centralized matching markets under incomplete information. We show that truth-telling is a Bayesian Nash equilibrium of the revelation game induced by a common belief and a stable mechanism if and only if all the profiles in the support of the common belief have singleton cores. Our result matches the observations of Roth and Peranson (1999) in the National Resident Matching Program (NRMP) in the United States: (i) the cores of the profiles submitted to the clearinghouse are small and (ii) while truth-telling is not a dominant strategy most participants of the NRMP truthfully reveal their preferences.Matching Market, Incomplete Information, Small Core

A MODEL OF IMMIGRATION, INTEGRATION AND CULTURAL TRANSMISSION OF SOCIAL NORMS

I present and study an evolutionary model of immigration and culturaltransmission of social norms in a set-up where agents are repeatedly matchedto play a one-shot interaction prisoner´s dilemma. Matching can be non-randomdue to limited integration (or population viscosity). The latter refers to atendency of individuals to have a higher rate of interaction with individuals oftheir type than with similar numbers of other agents. I derive a culturaltransmission mechanism in order to examine the influence of viscosity and ofother institutional characteristics of society on the evolutionary selection of prosocialnorms. The main findings are that strict norms, sustained by stronginternal punishment, need either viscosity or strong institutional pressures topersist, while norms of intermediate strength persist under a variety ofinstitutional characteristics. Endogenizing norm strength allows to identify twoscenarios in which pro-social norms survive: One of rigidity in whichseparation (high viscosity) leads to monomorphic equilibria with strict normsfor cooperation. And one of integration (low viscosity) where intermediatenorms persist in polymorphic equilibria. Furthermore, with endogenous norms,viscosity and cooperation are not linked in a monotone way.Cultural Evolution, Game Theory, Social Norms, Cooperation, Population Viscosity.

Constrained School Choice

Recently, several school districts in the US have adopted or consider adopting the Student-Optimal Stable mechanism or the Top Trading Cycles mechanism to assign children to public schools. There is evidence that for school districts that employ (variants of) the so-called Boston mechanism the transition would lead to efficiency gains. The first two mechanisms are strategy-proof, but in practice student assignment procedures typically impede a student to submit a preference list that contains all his acceptable schools. We study the preference revelation game where students can only declare up to a fixed number of schools to be acceptable. We focus on the stability and efficiency of the Nash equilibrium outcomes. Our main results identify rather stringent necessary and sufficient conditions on the priorities to guarantee stability or efficiency of either of the two mechanisms. This stands in sharp contrast with the Boston mechanism which has been abandoned in many US school districts but nevertheless yields stable Nash equilibrium outcomes.school choice, matching, stability, Gale-Shapley deferred acceptance algorithm, top trading cycles, Boston mechanism, acyclic priority structure, truncation

Mechanisms for efficient voting with private information about preferences

We experimentally study behavior in a simple voting game where players have private information about their preferences. With random matching, subjects overwhelmingly follow the dominant strategy to exaggerate their preferences, which leads to inefficiency. We analyze an exogenous linking mechanism suggested by Jackson and Sonnenschein (2007) as well as repeated interaction in different settings, which could allow endogenous linking mechanisms to evolve. We find that applying the exogenous mechanism captures nearly all achievable efficiency gains, whereas repeated interaction leads to significant gains in truthful representation and efficiency only in a setting where players can choose their partners. --Experimental Economics,Mechanism Design,Implementation,Linking,Bayesian Equilibrium,Efficiency

Credible Group Stability in Many-to-Many Matching Problems

It is known that in two-sided many-to-many matching problems, pairwise stable matchings may not be immune to group deviations, unlike in many- to-one matching problems (Blair 1988). In this paper, we show that pairwise stability is equivalent to credible group stability when one side has responsive preferences and the other side has categorywise- responsive preferences. A credibly group-stable matching is immune to any “executable” group deviations with an appropriate definition of executability. Under the same preference restriction, we also show the equivalence between the set of pairwise-stable matchings and the set of matchings generated by coalition-proof Nash equilibria of an appropriately defined strategic-form game.