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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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    Cited by:

    1. Vicki Knoblauch, 2020. "Von Neumann–Morgenstern stable set rationalization of choice functions," Theory and Decision, Springer, vol. 89(3), pages 369-381, October.
    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.

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