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On the solution of w-stable sets

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  • Han, Weibin
  • Van Deemen, Adrian

Abstract

The notion of m-stable sets was introduced in Peris and Subiza (2013) for abstract decision problems. Since it may lack internal stability and fail to discriminate alternatives in cyclic circumstances, we alter this notion, which leads to an alternative solution called w-stable set. Subsequently, we characterize w-stable set and compare it with other solutions in the literature. In addition, we propose a selection procedure to filter out more desirable w-stable sets.

Suggested Citation

  • Han, Weibin & Van Deemen, Adrian, 2016. "On the solution of w-stable sets," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 87-92.
    • Handle: RePEc:eee:matsoc:v:84:y:2016:i:c:p:87-92
    DOI: 10.1016/j.mathsocsci.2016.09.007
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    References listed on IDEAS

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    1. Thomas Quint & Jun Wako, 2004. "On Houseswapping, the Strict Core, Segmentation, and Linear Programming," Yale School of Management Working Papers ysm373, Yale School of Management.
    2. Subiza Begoña & Peris Josep E., 2014. "A Solution for General Exchange Markets with Indivisible Goods when Indifferences are Allowed," Mathematical Economics Letters, De Gruyter, vol. 2(3-4), pages 77-81, November.
    3. Peris, Josep E. & Subiza, Begoña, 2013. "A reformulation of von Neumann–Morgenstern stability: m-stability," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 51-55.
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    8. Thomas Quint & Jun Wako, 2004. "On Houseswapping, the Strict Core, Segmentation, and Linear Programming," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 861-877, November.
    9. Robert Delver & Herman Monsuur, 2001. "Stable sets and standards of behaviour," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 555-570.
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    Cited by:

    1. Atay, Ata & Núñez, Marina, 2019. "A note on the relationship between the core and stable sets in three-sided markets," Mathematical Social Sciences, Elsevier, vol. 98(C), pages 10-14.
    2. Han, Weibin & van Deemen, Adrian, 2021. "The solution of generalized stable sets and its refinement," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 60-67.
    3. Athanasios Andrikopoulos & Nikolaos Sampanis, 2024. "A topological characterization of the existence of w-stable sets," Papers 2403.04512, arXiv.org.
    4. Michele Gori, 2023. "Families of abstract decision problems whose admissible sets intersect in a singleton," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 61(1), pages 131-154, July.

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