IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v84y2016icp87-92.html
   My bibliography  Save this article

On the solution of w-stable sets

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165489616300956
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.mathsocsci.2016.09.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    3. 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 1-5, November.
    4. 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.
    5. 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.
    6. Lucas, William F., 1992. "Von Neumann-Morgenstern stable sets," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 17, pages 543-590, Elsevier.
    7. Christian Klamler, 2005. "The Copeland rule and Condorcet’s principle," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(3), pages 745-749, April.
    8. Roy, Bernard & Vincke, Philippe, 1981. "Multicriteria analysis: survey and new directions," European Journal of Operational Research, Elsevier, vol. 8(3), pages 207-218, November.
    9. Kalai, Ehud & Schmeidler, David, 1977. "An admissible set occurring in various bargaining situations," Journal of Economic Theory, Elsevier, vol. 14(2), pages 402-411, April.
    10. Kenneth J. Arrow & Herve Raynaud, 1986. "Social Choice and Multicriterion Decision-Making," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262511754, December.
    11. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Athanasios Andrikopoulos & Nikolaos Sampanis, 2024. "A topological characterization of the existence of w-stable sets," Papers 2403.04512, arXiv.org.
    3. 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.
    4. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Alcalde-Unzu, Jorge & Molis, Elena, 2011. "Exchange of indivisible goods and indifferences: The Top Trading Absorbing Sets mechanisms," Games and Economic Behavior, Elsevier, vol. 73(1), pages 1-16, September.
    3. 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 1-5, November.
    4. Weibin Han & Adrian Deemen & D. Ary A. Samsura, 2016. "A note on extended stable sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(2), pages 265-275, August.
    5. Di Feng & Bettina Klaus, 2022. "Preference revelation games and strict cores of multiple‐type housing market problems," International Journal of Economic Theory, The International Society for Economic Theory, vol. 18(1), pages 61-76, March.
    6. Alvin E Roth & Tayfun Sönmez & M. Utku Ünver, 2005. "Efficient Kidney Exchange: Coincidence of Wants in a Structured Market," Levine's Bibliography 784828000000000126, UCLA Department of Economics.
    7. Péter Biró & Flip Klijn & Xenia Klimentova & Ana Viana, 2021. "Shapley-Scarf Housing Markets: Respecting Improvement, Integer Programming, and Kidney Exchange," Working Papers 1235, Barcelona School of Economics.
    8. Rajnish Kunar & Kriti Manocha & Josue Ortega, 2020. "On the integration of Shapley-Scarf housing markets," Papers 2004.09075, arXiv.org, revised Jan 2022.
    9. Jaramillo, Paula & Manjunath, Vikram, 2012. "The difference indifference makes in strategy-proof allocation of objects," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1913-1946.
    10. Kumar, Rajnish & Manocha, Kriti & Ortega, Josué, 2022. "On the integration of Shapley–Scarf markets," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    11. Will Sandholtz & Andrew Tai, 2023. "House-Swapping with Objective Indifferences," Papers 2306.09529, arXiv.org.
    12. 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.
    13. Murat Yılmaz & Özgür Yılmaz, 2022. "Stability of an allocation of objects," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 561-580, December.
    14. Emilio Guaman & Juan Pablo Torres-Martinez, 2023. "Coalitional Stability and Incentives in Housing Markets with Incomplete Preferences," Working Papers wp547, University of Chile, Department of Economics.
    15. Athanasios Andrikopoulos & Nikolaos Sampanis, 2024. "A topological characterization of the existence of w-stable sets," Papers 2403.04512, arXiv.org.
    16. 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.
    17. Jinpeng Ma, 1998. "Strategic Formation of Coalitions," Departmental Working Papers 199810, Rutgers University, Department of Economics.
    18. Josep E., Peris & Begoña, Subiza, 2015. "Rationalizable Choice and Standards of Behavior," QM&ET Working Papers 15-5, University of Alicante, D. Quantitative Methods and Economic Theory.
    19. 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.
    20. Demuynck, Thomas & Herings, P. Jean-Jacques & Saulle, Riccardo & Seel, Christian, 2018. "The Myopic Stable Set for Social Environments (RM/17/002-revised)," Research Memorandum 001, Maastricht University, Graduate School of Business and Economics (GSBE).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matsoc:v:84:y:2016:i:c:p:87-92. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505565 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.