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Rational stability of choice functions

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  • Josep E. Peris
  • Begoña Subiza

Abstract

Two independent approaches have been used to analyze choices. A prominent notion is rationalizability: individuals choose maximizing binary relations. An alternative is to analyze choices in terms of standards of behavior with the notion of von Neumann–Morgenstern (vNM)‐stability. We introduce a new concept (r‐ $r \mbox{-} $stability) that in turn extends the notion of stability and rationality. Our main result establishes that every rationalizable choice function is r‐ $r \mbox{-} $stable and every vNM‐stable choice has an r‐ $r \mbox{-} $stable selection. An appealing property of r‐ $r \mbox{-} $stability is that well‐known solution concepts (top cycle, uncovered set, …) are r‐ $r \mbox{-} $stable, while they are neither rationalizable nor vNM‐stable.

Suggested Citation

  • Josep E. Peris & Begoña Subiza, 2023. "Rational stability of choice functions," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(3), pages 580-598, September.
    • Handle: RePEc:bla:ijethy:v:19:y:2023:i:3:p:580-598
    DOI: 10.1111/ijet.12369
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    References listed on IDEAS

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    1. Dutta, Bhaskar, 1988. "Covering sets and a new condorcet choice correspondence," Journal of Economic Theory, Elsevier, vol. 44(1), pages 63-80, February.
    2. Brandt, Felix, 2011. "Minimal stable sets in tournaments," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1481-1499, July.
    3. Peris, Josep E. & Subiza, Begona, 1994. "Maximal elements of not necessarily acyclic binary relations," Economics Letters, Elsevier, vol. 44(4), pages 385-388, April.
    4. Deb, Rajat, 1983. "Binariness and rational choice," Mathematical Social Sciences, Elsevier, vol. 5(1), pages 97-105, August.
    5. Laffond G. & Laslier J. F. & Le Breton M., 1993. "The Bipartisan Set of a Tournament Game," Games and Economic Behavior, Elsevier, vol. 5(1), pages 182-201, January.
    6. John C. Harsanyi, 1974. "An Equilibrium-Point Interpretation of Stable Sets and a Proposed Alternative Definition," Management Science, INFORMS, vol. 20(11), pages 1472-1495, July.
    7. 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.
    8. Vicki Knoblauch, 2020. "Von Neumann–Morgenstern stable set rationalization of choice functions," Theory and Decision, Springer, vol. 89(3), pages 369-381, October.
    9. Gilbert Laffond & Jean Lainé & Jean-François Laslier, 1996. "Composition-consistent tournament solutions and social choice functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 75-93, January.
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