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A Review of the Existence of Stable Roommate Matchings

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Abstract

We compare different preference restrictions that ensure the existence of a stable roommate matching. Some of these restrictions are generalized to allow for indifferences as well as incomplete preference lists, in the sense that an agent may prefer remaining single to matching with some agents. We also introduce a new type of cycles and in greater detail investigate the domain of preferences that have no such cycles. In particular, we show how the absence of these cycles relates to the "symmetric utilities hypothesis" by Rodrigues-Neto (Journal of Economic Theory 135, 2007) when applied to roommate problems with weak preferences.

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  • Gudmundsson, Jens, 2013. "A Review of the Existence of Stable Roommate Matchings," Working Papers 2013:8, Lund University, Department of Economics.
    • Handle: RePEc:hhs:lunewp:2013_008
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    File URL: http://project.nek.lu.se/publications/workpap/papers/WP13_8.pdf
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    1. Alvaro Rodrigues-Neto, Jose, 2007. "Representing roommates' preferences with symmetric utilities," Journal of Economic Theory, Elsevier, vol. 135(1), pages 545-550, July.
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    Cited by:

    1. Gudmundsson, Jens, 2013. "Cycles and Third-Party Payments in the Partnership Formation Problem," Working Papers 2013:16, Lund University, Department of Economics.

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    More about this item

    Keywords

    Roommate problem; existence; stable matching; cycles;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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