Equilibrium versions of variational principles in quasi-metric spaces and the robust trap problem

Jing-Hui Qiu (1) , Fei He (2) , Antoine Soubeyran (3)

1 Soochow University
2 THU - Tsinghua University [Beijing]
3 AMSE - Aix-Marseille Sciences Economiques

Using a pre-order principle in [Qiu JH. A pre-order principle and set-valued Ekeland variational principle. J Math Anal Appl. 2014;419:904–937], we establish a general equilibrium version of set-valued Ekeland variational principle (denoted by EVP), where the objective bimap is defined on the product of left-complete quasi-metric spaces and taking values in a quasi-order linear space, and the perturbation consists of the quasi-metric and a positive vector . Here, the ordering is only to be -closed, which is strictly weaker than to be topologically closed. From the general equilibrium version, we deduce a number of particular equilibrium versions of EVP with set-valued bimaps or with vector-valued bimap. As applications of the equilibrium versions of EVP, we present several interesting results on equilibrium problems, vector optimization and fixed point theory in the setting of quasi-metric spaces. These results extend and improve the related known results. Using the obtained EVPs, we further study the existence and the robustness of traps in Behavioural Sciences.

Domains: Humanities and Social Sciences; Economics and Finance; Mathematics [math]

Jing-Hui Qiu, Fei He, Antoine Soubeyran. Equilibrium versions of variational principles in quasi-metric spaces and the robust trap problem. Optimization, 2017, 67 (1), pp.25-53. ⟨10.1080/02331934.2017.1387257⟩. ⟨hal-02084464⟩