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Generalized matchings for preferences represented by simplest semiorder: Stability and pareto optimality

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Abstract

We consider an extension of the classical model of generalized Gale-Shapley matchings. The model describes a two-sided market: on one side, universities each of which has a restriction on the number of enrolled students; on the other side, applicants each of which can get a single place in the university. Both applicants and universities have preferences with respect to the desired distribution. We assume that each applicant constructs a linear order on the set of desired universities, and each university has preferences that are simplest semiorders For this modification, we show that a stable matching always exists. Moreover, we formulate necessary and sufficient conditions for Pareto optimality of the stable matching.

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Authors and Affiliations

  1. National Research University Higher School of Economics, Moscow, Russia

    S. G. Kisel’gof

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  1. S. G. Kisel’gof
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Correspondence to S. G. Kisel’gof.

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Original Russian Text © S.G. Kisel’gof, 2014, published in Avtomatika i Telemekhanika, 2014, No. 6, pp. 103–114.

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Kisel’gof, S.G. Generalized matchings for preferences represented by simplest semiorder: Stability and pareto optimality. Autom Remote Control 75, 1069–1077 (2014). https://doi.org/10.1134/S0005117914060071

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  • DOI: https://doi.org/10.1134/S0005117914060071

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