Rational stability of choice functions

Josep E. Peris and Begoña Subiza

International Journal of Economic Theory, 2023, vol. 19, issue 3, 580-598

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.

Date: 2023
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