Abstract
In this paper, we consider a one-to-one matching model with two phases; an adolescence phase where individuals meet a number of dates and learn about their aspirations, followed by a matching phase where individuals are matched according to a version of Gale and Shapley’s (Am Math Mon 69:9–15, 1962) deferred acceptance (DA) algorithm. Using simulations of this model, we study how the likelihoods of matching and divorce, and also the balancedness and the speed of matching associated with the outcome of the DA algorithm are affected by the size of correlation in the preferences of individuals and by the frequency individuals update their aspirations in the adolescence phase.
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Notes
See, for example, Roth (1984, 2002, 2008) for the earliest known inventions as well as many practical uses of this algorithm by the National Resident Matching Program in the United States and by regional medical markets elsewhere. Discussions on similar uses of the algorithm can also be found in Balinski and Sönmez (1999), dealing with the problem of student placement (or centralized school admissions) that is known to exist in several countries including China, Greece, and Turkey, and in Abdulkadirog̃lu et al. (2005) and Pathak and Sönmez (2008) dealing with matching problems in the New York City high schools and Boston public schools, respectively.
Moreover, as was shown by Gale and Shapley (1962), if all men and women have strict preferences, then the DA algorithm with men proposing always produces men-optimal stable matching; i.e. a stable matching which all men weakly prefer to any other stable matching. Since the focus of our paper will not be on the optimality of stable matchings; we will allow individuals to have indifference in their preference relations.
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Saglam, I. The Success of the Deferred Acceptance Algorithm Under Heterogenous Preferences with Endogenous Aspirations. Comput Econ 57, 577–591 (2021). https://doi.org/10.1007/s10614-020-09969-1
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DOI: https://doi.org/10.1007/s10614-020-09969-1