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Group Strategyproof Pareto-Stable Marriage with Indifferences via the Generalized Assignment Game

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Algorithmic Game Theory (SAGT 2017)

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Abstract

We study the variant of the stable marriage problem in which the preferences of the agents are allowed to include indifferences. We present a mechanism for producing Pareto-stable matchings in stable marriage markets with indifferences that is group strategyproof for one side of the market. Our key technique involves modeling the stable marriage market as a generalized assignment game. We also show that our mechanism can be implemented efficiently. These results can be extended to the college admissions problem with indifferences.

This research was supported by NSF Grant CCFā€“1217980.

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Notes

  1. 1.

    The algorithm of Erdil and Ergin proceeds in two phases. In the first phase, ties are broken arbitrarily and the deferred acceptance algorithm is used to obtain a weakly stable matching. In the second phase, a sequence of Pareto-improvements are applied until a Pareto-stable matching is reached. In App. A in the full version of [7], we show that this algorithm does not provide a strategyproof mechanism.

  2. 2.

    A stable mechanism can be strategyproof only for the side having unit demand, namely the students [20].

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Correspondence to Nevzat Onur DomaniƧ , Chi-Kit Lam or C. Gregory Plaxton .

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DomaniƧ, N.O., Lam, CK., Plaxton, C.G. (2017). Group Strategyproof Pareto-Stable Marriage with Indifferences via the Generalized Assignment Game. In: BilĆ², V., Flammini, M. (eds) Algorithmic Game Theory. SAGT 2017. Lecture Notes in Computer Science(), vol 10504. Springer, Cham. https://doi.org/10.1007/978-3-319-66700-3_22

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  • DOI: https://doi.org/10.1007/978-3-319-66700-3_22

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