Greta Lamonaca, Uniqueness and non-uniqueness for harvesting mean field games

par Mlle Greta Lamonaca (Institut Denis Poisson, CEREMADE)

jeudi 12 févr. 2026, 10:30 → 12:30 Europe/Paris

Salle de Séminaire (IDP-Orléans)

Sustainable harvesting of natural resources is a central challenge both in ecology and economics. In this presentation, we qualitatively explore the role of human actions in the decline of biodiversity, focusing on the problem of fishing in a bounded domain. More precisely, we consider a population of fishermen whose actions influence, and are influenced by, the dynamics of a fish population. Two distinct scenario are considered: in the framework of the Mean Field Game (MFG), fishermen act competitively to maximize their individual income, while in the context of Mean Field Control (MFC) they cooperate under a central planner to maximize a common objective. We will combine reaction diffusion equations and MFG theory to model and analyze the two resulting fishing systems. 
Our analysis focuses mainly on ergodic (static) systems, since the study of the uniqueness regimes for the limit (static) system is essential to characterize the long-time behavior of the evolutionary model. Particular attention is given to the comparison between MFG and MFC: we will investigate the attractiveness of the unique static solution in the competitive scenario, and regimes where, instead, multiple solutions occur in the cooperative setting and the variables that seem to determine these different phenomena.