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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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