Rational stability of choice functions

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‐stability) that in turn extends the notion of stability and rationality. Our main result establishes that every rationalizable choice function is r‐stable and every vNM‐stable choice has an r‐stable selection. An appealing property of r‐stability is that well-known solution concepts (top cycle, uncovered set, …) are r‐stable, while they are neither rationalizable nor vNM‐stable.