AVVISO di SEMINARIO Prof. Paolo Dai Pra Università di Verona TITOLO Polarization and Coherence in Mean Field Games Driven by Private and Social Utility 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. Joint work with Marco Tolotti (Venezia) and Elena Sartori (Padova). Il seminario si terrà il giorno 13 Gennaio 2023 ore 11:00 nella Aula F del Dipartimento Matematica e Applicazioni, Università di Napoli FEDERICO II, Complesso di Monte Sant'Angelo, Via Cintia, Napoli. Link a Teams: https://teams.microsoft.com/l/meetup-join/19%3aMQ4RZDBo_0G-K_PHxKtktVYAczOGb... -- Enrica Pirozzi Dipartimento di Matematica e Applicazioni Universita' di Napoli FEDERICO II Via Cintia, Monte S.Angelo, 80126, NAPOLI, ITALY Tel. 081 675634 https://www.docenti.unina.it/ENRICA.PIROZZI