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A note on extended stable sets

Author

Listed:
  • Weibin Han

    (Radboud University Nijmegen)

  • Adrian Deemen

    (Radboud University Nijmegen)

  • D. Ary A. Samsura

    (Radboud University Nijmegen)

Abstract

We study abstract decision problems by introducing an extended dominance relation with respect to a set of alternatives. This extension is in between the traditional dominance relation as formulated by Von Neumann and Morgenstern (Theory of games and economic behavior, Princeton University Press, Princeton, 1944) and the transitive closure of it. Subsequently, stable sets are defined and studied for this extended relation. We formulate a characterization of stable sets for this relation and an existence theorem. Finally, we discuss its relation with Von Neumann–Morgenstern stable sets and generalized stable sets.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sochwe:v:47:y:2016:i:2:d:10.1007_s00355-016-0958-z
    DOI: 10.1007/s00355-016-0958-z
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    References listed on IDEAS

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    1. Elena Inarra & Jeroen Kuipers & N. Olaizola, 2005. "Absorbing and generalized stable sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(3), pages 433-437, June.
    2. 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.
    3. Kalai, Ehud & Pazner, Elisha A & Schmeidler, David, 1976. "Collective Choice Correspondences as Admissible Outcomes of Social Bargaining Processes," Econometrica, Econometric Society, vol. 44(2), pages 233-240, March.
    4. John Duggan, 2013. "Uncovered sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(3), pages 489-535, September.
    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. 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.
    8. Houy Nicolas, 2009. "More on the stable, generalized stable, absorbing and admissible sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(4), pages 691-698, November.
    9. Elizabeth Penn, 2006. "The Banks Set in Infinite Spaces," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(3), pages 531-543, December.
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    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. Vicki Knoblauch, 2020. "Von Neumann–Morgenstern stable set rationalization of choice functions," Theory and Decision, Springer, vol. 89(3), pages 369-381, October.

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