A Microeconomic Application of Mean Field Game Theory

In this Thesis we overview of the mathematical theory of Mean Field Games and provide an application of this theory to Microeconomics. The first three chapters are devoted to the formalism of Mean Field Games, with an emphasis on the Propagation of Chaos to justify the asymptotic approximation of a continuous system of players. Following the analytical approach, we characterize the Nash Equilibria in Mean Field Games by a forward-backward system of partial differential equations (Hamilton-Jacobi-Bellman, Fokker-Planck). In Chapter 4, we revisit a mean-field game problem proposed in a recent paper, modelling the price formation arising as an equilibrium within an oligopoly market made up by firms competing through the production of the same good and influencing each other through the average aggregate level of production. In Chapter 5, we generalize the model allowing for more general structure of aggregation depend on higher moments of the production; we will characterize the equilibria as solutions to a system of integro-differential equations, for which we provide an existence result, solving it numerically.