Seminario

Polarization and Coherence in Mean Field Games Driven by Private and Social Utility

Seminario all'interno dell' Informal scientific meeting "Controllo di dinamiche e flussi e applicazioni socio-logistico-economic
2 dicembre 2022
Orario di inizio 
09:30
PovoZero - Via Sommarive 14, Povo (Trento)
Aula Seminari "-1"
Organizzato da: 
Dipartimento di Matematica
Destinatari: 
Comunità universitaria
Partecipazione: 
Ingresso libero
Referente: 
Prof. Fabio Bagagiolo
Contatti: 
Staff Dipartimento di Matematica
0461/281508-1625-1701-3898-1980
Speaker: 
Marco Tolotti (Università di Venezia)

Abstract: We study a mean field game in continuous time over a finite horizon, T, where the state of each agent is binary and where players base their strategic decisions on two, possibly competing, factors: the willingness to align with the majority (conformism) and the aspiration of sticking with the own type (stubbornness). We also consider a quadratic cost related to the rate at which a change in the state happens: changing opinion may be a costly operation. Depending on the parameters of the model, the game may have more than one Nash equilibrium, even though the corresponding N-player game does not. Moreover, it exhibits a very rich phase diagram, where polarized/unpolarized, coherent/incoherent equilibria may coexist, except for T small, where the equilibrium is always unique. We fully describe such phase diagram in closed form and provide a detailed numerical analysis of the N-player counterpart of the mean field game. In this finite dimensional setting, the equilibrium selected by the population of players is always coherent (favor- ing the subpopulation whose type is aligned with the initial condition), but it does not necessarily minimize the cost functional. Rather, it seems that, among the coherent ones, the equilibrium prevailing is the one that most benefits the underdog subpopulation forced to change opinion. Joint work with Paolo Dai Pra (Verona) and Elena Sartori (Padova).