On Stationary Mean-field Games with Singular Controls

Ferrari Giorgio, Center for Mathematical Economics (IMW), Bielefeld University

In this talk we present some recent results on stationary mean-field games with singular controls. The mean-field interaction comes through the stationary distribution of a singularly controlled state variable, which follows an It\^o dynamics with drift and volatility coefficients possibly depending on a continuous-time Markov chain. We show existence and uniqueness of the equilibrium for the considered classes of mean-field games and we prove that the mean-field solution approximates Nash equilibria of related $N$-player games. The talk is based on works with Haoyang Cao, Jodi Dianetti, and Ioannis Tzouanas.

Area: CS3 - Mean Field Games and Mean Field Control II (Andrea Cosso & Luciano Campi)

Keywords: mean-field games; singular stochastic control; ergodic performance criterion; (regime-switching) It\ô-diffusions; free boundary

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