4,895 research outputs found
Manipulation of Stable Matchings using Minimal Blacklists
Gale and Sotomayor (1985) have shown that in the Gale-Shapley matching
algorithm (1962), the proposed-to side W (referred to as women there) can
strategically force the W-optimal stable matching as the M-optimal one by
truncating their preference lists, each woman possibly blacklisting all but one
man. As Gusfield and Irving have already noted in 1989, no results are known
regarding achieving this feat by means other than such preference-list
truncation, i.e. by also permuting preference lists.
We answer Gusfield and Irving's open question by providing tight upper bounds
on the amount of blacklists and their combined size, that are required by the
women to force a given matching as the M-optimal stable matching, or, more
generally, as the unique stable matching. Our results show that the coalition
of all women can strategically force any matching as the unique stable
matching, using preference lists in which at most half of the women have
nonempty blacklists, and in which the average blacklist size is less than 1.
This allows the women to manipulate the market in a manner that is far more
inconspicuous, in a sense, than previously realized. When there are less women
than men, we show that in the absence of blacklists for men, the women can
force any matching as the unique stable matching without blacklisting anyone,
while when there are more women than men, each to-be-unmatched woman may have
to blacklist as many as all men. Together, these results shed light on the
question of how much, if at all, do given preferences for one side a priori
impose limitations on the set of stable matchings under various conditions. All
of the results in this paper are constructive, providing efficient algorithms
for calculating the desired strategies.Comment: Hebrew University of Jerusalem Center for the Study of Rationality
discussion paper 64
The Internal Job Market of the IMF's Economist Program
This paper shows how the internal job market for participants in the IMF's Economist Program (EPs) could be redesigned to eliminate most of the shortcomings of the current system. The new design is based on Gale and Shapley's (1962) deferred acceptance algorithm and generates an efficient and stable outcome. An Excel-based computer program, EP-Match, implements the algorithm and applies it to the internal job market for EPs. The program can be downloaded from http://www.people.hbs.edu/gbarron/EP-Match_for_Excel.htm. Copyright 2005, International Monetary Fund
Implementing quotas in university admissions: An experimental analysis
Quotas for special groups of students often apply in school or university admission procedures. This paper studies the performance of two mechanisms to implement such quotas in a lab experiment. The first mechanism is a simplified version of the mechanism currently employed by the German central clearinghouse for university admissions, which first allocates seats in the quota for top-grade students before allocating all other seats among remaining applicants. The second is a modied version of the student-proposing deferred acceptance (SDA) algorithm, which simultaneously allocates seats in all quotas. Our main result is that the current procedure, designed to give top-grade students an advantage, actually harms them, as students often fail to grasp the strategic issues involved. The modified SDA algorithm significantly improves the matching for top-grade students and could thus be a valuable tool for redesigning university admissions in Germany.College admissions, experiment, quotas, matching; Gale-Shapley mechanism, Boston mechanism
Implementing quotas in university admissions: An experimental analysis
Quotas for special groups of students often apply in school or university admission procedures. This paper studies the performance of two mechanisms to implement such quotas in a lab experiment. The first mechanism is a simplified version of the mechanism currently employed by the German central clearinghouse for university admissions, which first allocates seats in the quota for top-grade students before allocating all other seats among remaining applicants. The second is a modified version of the student-proposing deferred acceptance (SDA) algorithm, which simultaneously allocates seats in all quotas. Our main result is that the current procedure, designed to give top-grade students an advantage, actually harms them, as students often fail to grasp the strategic issues involved. The modified SDA algorithm significantly improves the matching for top-grade students and could thus be a valuable tool for redesigning university admissions in Germany. --college admissions,experiment,quotas,matching,Gale-Shapley mechanism,Boston mechanism
Acyclicity and singleton cores in matching markets
This paper analyzes the role of acyclicity in singleton cores. We show that the absence of simultaneous cycles is a sufficient condition for the existence of singleton cores. Furthermore, acyclicity in the preferences of either side of the market is a minimal condition that guarantees the existence of singleton cores. If firms or workers preferences are acyclical, unique stable matching is obtained through a procedure that resembles a serial dictatorship. Thus, acyclicity generalizes the notion of common preferences. It follows that if the firms or workers preferences are acyclical, unique stable matching is strongly efficient for the other side of the marketStable matching, Acyclicity, Singleton cores
Fee-Setting Mechanisms: On Optimal Pricing by Intermediaries and Indirect Taxation
Mechanisms according to which private intermediaries or governments charge
transaction fees or indirect taxes are prevalent in practice. We consider a setup with
multiple buyers and sellers and two-sided independent private information about
valuations. We show that any weighted average of revenue and social welfare can be
maximized through appropriately chosen transaction fees and that in increasingly
thin markets such optimal fees converge to linear fees. Moreover, fees decrease with
competition (or the weight on welfare) and the elasticity of supply but decrease
with the elasticity of demand. Our theoretical predictions fit empirical observations
in several industries with intermediaries
Clearinghouses for two-sided matching: An experimental study
We experimentally study the Gale and Shapley, 1962 mechanism, which is utilized in a wide set of applications, most prominently the National Resident Matching Program (NRMP). Several insights come out of our analysis. First, only 48% of our observed outcomes are stable, and among those a large majority culminate at the receiver-optimal stable matching. Second, receivers rarely truncate their true preferences: it is the proposers who do not make offers in order of their preference, frequently skipping potential partners. Third, market characteristics affect behavior: both the cardinal representation and core size influence whether laboratory outcomes are stable. We conclude by using our controlled results and a behavioral model to shed light on a number of stylized facts we derive from new NRMP survey and outcome data, and to explain the small cores previously documented for the NRMP
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