Variable preference relations: existence of maximal elements

The Luc Dinh (1) , Antoine Soubeyran (2)

1 LANLG - Laboratoire d'Analyse non linéaire et Géométrie
2 GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille

We consider variable preference relations, called also reference depen- dent preference relations which are typical in the study of dynamic models in economic theories. Elementary properties of variable preference rela- tions are established including consistency and acyclicity. The main result of the paper is on an existence criterion for maximal elements of a set equipped with a variable preference relation. It is proven in a rather sim- ple way, but generalizes a number of results known in the recent literature on maximum principles on a space with or without topological structure.

Mots clés: Variable preference relation; improving path; maximal point; maximum principle.; maximum principle

Domaines: Optimisation et contrôle [math.OC]

The Luc Dinh, Antoine Soubeyran. Variable preference relations: existence of maximal elements. 2010. ⟨hal-00621272⟩