COMPUTATION OF MEAN FIELD EQUILIBRIA IN ECONOMICS

Aimé Lachapelle (1) , Julien Salomon (1) , Gabriel Turinici (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

Motivated by a mean field games stylized model for the choice of technologies (with externalities and economy of scale), we consider the associated optimization problem and prove an existence result. To complement the theoretical result, we introduce a monotonic algorithm to find the mean field equilibria. We close with some numerical results, including the multiplicity of equilibria describing the possibility of a technological transition.

Mots clés: mean field games; dynamic equilibrium; externalities; monotonic algorithms; optimal control; non-convex optimization

Domaines: Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]

Aimé Lachapelle, Julien Salomon, Gabriel Turinici. COMPUTATION OF MEAN FIELD EQUILIBRIA IN ECONOMICS. 2008. ⟨hal-00346214v1⟩