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This paper analyzes problems in which a large benevolent player, controlling a set of policy variables, maximizes aggregate welfare in a continuous-time economy populated by atomistic agents subject to idiosyncratic shocks. We first provide as a benchmark the social optimum solution, in which a...
The goal of the paper is to introduce a formulation of the mean field game with major and minor players as a fixed point on a space of controls. This approach emphasizes naturally the role played by McKean–Vlasov dynamics in some of the players’ optimization problems. We apply this approach to...
In this article, we provide the first systemic study on discrete time partially observable mean field systems in the presence of a common noise. Each player makes decision solely based on the observable process. Both the mean field games and the related tractable mean field type stochastic...
The paper studies the convergence, as N tends to infinity, of a system of N coupled Hamilton–Jacobi equations, the Nash system, when the coupling between the players becomes increasingly singular. The limit equation turns out to be a mean field game system with a local coupling.
The goal of the paper is to introduce a set of problems which we call mean field games of timing. We motivate the formulation by a dynamic model of bank run in a continuous-time setting. We briefly review the economic and game theoretic contributions at the root of our effort, and we develop a...
In this paper we model the role of a government of a large population as a mean field optimal control problem. Such control problems are constrained by a PDE of continuity-type, governing the dynamics of the probability distribution of the agent population. We show the existence of mean field...
Time change is a powerful technique for generating noises and providing flexible models. In the framework of time changed Brownian and Poisson random measures we study the existence and uniqueness of a solution to a general mean-field stochastic differential equation. We consider a mean-field...
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