Variational Analysis in Cone Pseudo-Quasimetric Spaces and Applications to Group Dynamics

Truong Bao (1) , Antoine Soubeyran (2)

1 Northern Michigan University
2 GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille

In this paper, we generalize Ekeland’s variational principle in the new context of cone pseudo-quasimetric spaces. We propose this extension for applications to group dynamics in behavioral sciences. In this setting, a cone pseudo-quasimetric helps to model, in a crude way, multidimensional aspects of resistance to change for a group, where each component represents resistance to change of one agent in the group. At the behavioral level, our new version of Ekeland’s variational principle shows how a group, forming and breaking routines each period by balancing between motivations and resistances to change of all members, can improve step by step their payoffs to end in a trap worthwhile to approach and reach, but not worthwhile to leave.

Domaines: Economies et finances; Mathématiques [math]; Sciences de l'Homme et Société

Truong Bao, Antoine Soubeyran. Variational Analysis in Cone Pseudo-Quasimetric Spaces and Applications to Group Dynamics. Journal of Optimization Theory and Applications, 2016, 170 (2), pp.458 - 475. ⟨10.1007/s10957-016-0933-y⟩. ⟨hal-01690179⟩