Tandem concavity with application to matching problems

As a generalization of ordinal concavity we introduce a new notion of discrete concavity called tandem concavity defined for a function over the subsets of a finite set E endowed with an ordered partition ( E 1 , E 2 ) . Every function expressed as a lexicographic composition of two ordinally concave functions satisfies tandem concavity. We apply tandem concavity to the rationalization of choice rules in stable matching problems. We show that tandem concavity rationalizes a wider class of choice rules than ordinal concavity.