Gale-Shapley Mechanism Research Articles

Transparency and Fairness in School Choice Mechanisms

This article explores the impact of procedural information on the behavior of applicants under two of the most commonly used school admissions procedures: the Gale-Shapley mechanism and the Boston mechanism. In a lab experiment, I compare the impact of information about the mechanism, information about individually optimal application strategies, and information about both. I find that strategic and full information increase truth-telling and stability under the Gale-Shapley mechanism. Under the Boston mechanism, however, the adoption of equilibrium strategies remains unaffected. Contrary to prevailing assumptions in matching theory, I show that the Boston mechanism improves perceived fairness. These results underscore the importance of procedural information and suggest that eliminating justified envy may not be a sucient condition of fairness.

Transparency and Fairness in School Choice Mechanisms

This article explores the impact of procedural information on the behavior of applicants under two of the most commonly used school admissions procedures: the Gale-Shapley mechanism and the Boston mechanism. In a lab experiment, I compare the impact of information about the mechanism, information about individually optimal application strategies, and information about both. I find that strategic and full information increase truth-telling and stability under the Gale-Shapley mechanism. Under the Boston mechanism, however, the adoption of equilibrium strategies remains unaffected. Contrary to prevailing assumptions in matching theory, I show that the Boston mechanism improves perceived fairness. These results underscore the importance of procedural information and suggest that eliminating justified envy may not be a sufficient condition of fairness.

Incentive Compatibility of Large Centralized Matching Markets

We study the manipulability of stable matching mechanisms. To quantify incentives to manipulate stable mechanisms, we consider markets with random cardinal utilities, which induce ordinal preferences over match partners. We show that most agents in large matching markets are close to being indifferent of overall stable matchings. In one-to-one matching, the utility gain by manipulating a stable mechanism does not exceed the gap between utilities from the best and worst stable partners. Thus, most agents in a large market would not have significant incentives to manipulate stable mechanisms. The incentive compatibility extends to many-to-one matching when agents employ truncation strategies and capacity manipulations in a Gale—Shapley mechanism.

Two-Sided Matching with Endogenous Preferences

We modify the stable matching problem by allowing agents' preferences to depend on the endogenous actions of agents on the other side of the market. Conventional matching theory results break down in the modified setup. In particular, every game that is induced by a stable matching mechanism (e.g., the Gale-Shapley mechanism) may have equilibria that result in matchings that are not stable with respect to the agents' endogenous preferences. However, when the Gale-Shapley mechanism is slightly modified, every equilibrium of its induced game results in a pairwise stable matching with respect to the endogenous preferences as long as they satisfy a natural reciprocity property. (JEL C78, D82)

Group Strategy-Proofness in Private Good Economies Without Money: Matching, Division and House Allocation

We observe that three salient solutions to matching, division and house allocation problems are not only (partially) strategy-proof, but (partially) group strategy-proof as well, in appropriate domains of definition. That is the case for the Gale-Shapley mechanism, the uniform rule and the top trading cycle solution, respectively. We embed these three types of problems into a general framework. We then notice that the three rules, as well as many others, do share a common set of properties, which together imply their (partial) group strategy-proofness. This proves that the equivalence between individual and group strategy-proofness in all these cases is not a fortuitous event, but results from the structure of the functions under consideration.

Preference intensities and risk aversion in school choice: a laboratory experiment

We experimentally investigate in the laboratory prominent mechanisms that are employed in school choice programs to assign students to public schools and study how individual behavior is influenced by preference intensities and risk aversion. Our main results show that (a) the Gale–Shapley mechanism is more robust to changes in cardinal preferences than the Boston mechanism independently of whether individuals can submit a complete or only a restricted ranking of the schools and (b) subjects with a higher degree of risk aversion are more likely to play “safer” strategies under the Gale–Shapley but not under the Boston mechanism. Both results have important implications for enrollment planning and the possible protection risk averse agents seek.

Preference Intensities and Risk Aversion in School Choice: A Laboratory Experiment

We experimentally investigate in the laboratory two prominent mechanisms that are employed in school choice programs to assign students to public schools. We study how individual behavior is influenced by preference intensities and risk aversion. Our main results show that (a) the Gale–Shapley mechanism is more robust to changes in cardinal preferences than the Boston mechanism independently of whether individuals can submit a complete or only a restricted ranking of the schools and (b) subjects with a higher degree of risk aversion are more likely to play “safer” strategies under the Gale–Shapley but not under the Boston mechanism. Both results have important implications for the efficiency and the stability of the mechanisms.

Research Note—Improving the Efficiency of Course Bidding at Business Schools: Field and Laboratory Studies

Registrars' offices at most universities face the daunting task of allocating course seats to students. Because demand exceeds supply for many courses, course allocation needs to be done equitably and efficiently. Many schools use bidding systems in which student bids are used both to infer preferences over courses and to determine student priorities for courses. However, this dual role of bids can result in course allocations not being market outcomes, and in unnecessary efficiency loss, which can potentially be avoided with the use of an appropriate market mechanism. We report the result of field and laboratory studies that compare a typical course-bidding mechanism with the alternate Gale-Shapley Pareto-dominant market mechanism. Results from the field study (conducted at the Ross School of Business, University of Michigan) suggest that using the latter could vastly improve efficiency of course allocation systems while facilitating market outcomes. Laboratory experiments with greater design control confirm the superior efficiency of the Gale-Shapley mechanism. The paper tests theory that has important practical implications because it has the potential to affect the learning experience of very large numbers of students enrolled in educational institutions.

School choice and information: An experimental study on matching mechanisms

We present an experimental study where we analyze three well-known matching mechanisms—the Boston, the Gale–Shapley, and the Top Trading Cycles mechanisms—in different informational settings. Our experimental results are consistent with the theory, suggesting that the TTC mechanism outperforms both the Boston and the Gale–Shapley mechanisms in terms of efficiency and it is slightly more successful than the Gale–Shapley mechanism regarding the proportion of truthful preference revelation, whereas manipulation is stronger under the Boston mechanism. In addition, even though agents are much more likely to revert to truth-telling in lack of information about the others' payoffs—ignorance may be beneficial in this context—the TTC mechanism results less sensitive to the amount of information that participants hold. These results therefore suggest that the use of the TTC mechanism in practice is more desirable than of the others.

Implementation of Stable Solutions to Marriage Problems

This note analyzes the possibility of implementing stable outcomes for marriage markets. Our first result shows a contradiction between the use of stable mechanisms and the hypothesis of agents' behavior considered in the Nash equilibrium concept. We analyze the possibility of implementing two sets of stable allocations, by employing two types of mechanisms. The first mechanism is a “now-or-never” choice process that permits us to implement in undominated Nash equilibria the set of all the stable allocations. The second choice process is the classic algorithm in matching theory, the Gale–Shapley mechanism. A reversal property is observed in such a mechanism when agents act strategically. The use of a mechanism which selects the best solution for one side of the market in the absence of strategic behavior yields the best stable solution for the agents on the other side under dominance solvability.Journal of Economic LiteratureClassification Numbers: C72, D78, J41.