Fixed Points and Variational Principles with Applications to Capability Theory of Wellbeing via Variational Rationality

Abstract

In this paper we first develop two new results of variational analysis. One is a fixed point theorem for parametric dynamic systems in quasimetric spaces, which can also be interpreted as an existence theorem of minimal points with respect to reflexive and transitive preferences for sets in products spaces. The other one is a variational principle for set-valued mappings acting from quasimetric spaces to vector spaces with variable ordering structures, which can be treated as a far-going extension of Ekeland’s variational principle to this setting. Both of these results are motivated by applications to adaptive dynamical aspects of Sen’s capability theory of wellbeing. As consequence of our mathematical results, we develop new applications to such human behavioral models by using a recent variational rationality approach to behavioral sciences.