Choosing VNM-stable sets of the revealed dominance digraph

The choice functions that are consistent with selections of VNM-stable sets of an underlying revealed dominance digraph are characterized both under VNM-perfection of the latter and in the general case.VNM-stable sets, kernel-perfect digraphs, choice func-tions 1

Minimal covering set solutions

We study necessary and sufficient conditions for a multi-valued solution S to be rationalized in the following sense: there exists a complete asymmetric relation T (a tournament) such that, for each feasible (finite) set, the solution set of S coincides with the minimal covering set of T restricted to that feasible set. Our characterization result relies only on properties relating S across feasible choice sets