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Cheating Strategies for the Gale-Shapley Algorithm with Complete Preference Lists

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Abstract

This paper deals with a strategic issue in the stable marriage model with complete preference lists (i.e., a preference list of an agent is a permutation of all the members of the opposite sex).

Given complete preference lists of all the men, a partial marriage, and complete preference lists of unmatched women, we consider the problem of finding preference lists of matched women such that the men-proposing Gale-Shapley algorithm applied to the lists produces a (perfect) marriage which is an extension of a given partial marriage. We propose a polynomial time algorithm for finding a desired set of preference lists, if these exist.

We also deal with the case that complete preference lists of all the men and a partial marriage are given. In this case, we consider a problem of the existence of preference lists of all the women such that the men-proposing Gale-Shapley algorithm produces a marriage including a given partial marriage. We show NP-completeness of this problem.

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Authors and Affiliations

  1. Faculty of Science and Engineering, Chuo University, Kasuga, Bunkyo-ku, Tokyo, 112-8551, Japan

    Hirotatsu Kobayashi & Tomomi Matsui

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  1. Hirotatsu Kobayashi
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  2. Tomomi Matsui
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Correspondence to Tomomi Matsui.

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Kobayashi, H., Matsui, T. Cheating Strategies for the Gale-Shapley Algorithm with Complete Preference Lists. Algorithmica 58, 151–169 (2010). https://doi.org/10.1007/s00453-009-9359-3

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  • DOI: https://doi.org/10.1007/s00453-009-9359-3

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