RAVIEP
Recent Advances in Variational Inequalities and Equilibrium Problems II

Invited Session

Time Slot: Wednesday Afternoon

Room: 001

Chair: Laura Scrimali

On the equivalence between constrained variational problems

Time: 15:40

Sofia Giuffrè (DIIES, Mediterranea University of Reggio Calabria), Attilio Marcianò

The talk deals with nonlinear monotone variational inequalities with gradient constraints. In particular, using a new strong duality principle, we prove the equivalence of the problem under consideration with a double obstacle problem and with a Lagrange multiplier problem.

Quasi-variational problems with non-self map on Banach space

Time: 16:00

Domenico Scopelliti (University of Brescia, Brescia, Italy)

This talk focuses on the study of generalized quasi-variational inequality problemswith a non-self constraint map. For such problems, the concept of the projectedsolution needs to be introduced. The main result deals with the existence of suchsolutions on real Banach spaces. Then, we introduce the concept of the projectedsolution for a multistage stochastic generalized quasi-variational inequality, and the existence ofsuch a solution is provided. These theoretical results are applied in studying anelectricity market with renewable power sources.

A multiclass network international migration model under shared regulations

Time: 16:20

Fabio Raciti (Department of Mathematics and Computer Science, University of Catania), Mauro Passacantando

In this note we extend a previously proposed model of international human migration by introducing the possibility that some of the destination countries agree to establish a common upper bound on the migratory flows they are willing to accept jointly. In this framework, we propose a new equilibrium definition and prove its equivalence to a suitably defined variational inequality. Some numerical examples show that the flow distribution under joint regulations can differ from those corresponding to a situation where each government autonomously establishes migration bounds

Time-Dependent Generalized Nash Equilibria in Social Media Platforms

Time: 16:40

Georgia Fargetta (Department of Mathematics and Computer Science, University of Catania), Laura Scrimali

In this paper, we develop a dynamic network model of the competition of digital contents on social media platforms, assuming that there is a known and fixed upper bound on the total amount of views. In particular, we consider a two-layer network consisting of creators and viewers. Each creator seeks to maximize the profit by determining views and likes. The problem is formulated as a time-dependent generalized Nash equilibrium for which we provide the associated evolutionary variational inequality, using the variational equilibrium concept. We also discuss a possible differential game formulation. Finally, using a discrete-time approximation of the continuous time adjustment process, we present a numerical example.