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Rene Carmona : Mean Field Games: theory and applications (Mar 10, 2016 4:25 PM)

We review the Mean Field Game (MFG) paradigm introduced independently by Caines-Huang-Malhame and Lasry Lyons ten years ago, and we illustrate the relevance for applications with a couple of examples (bird flocking and room exit). We then review the probabilistic approach based on Forward-Backward Stochastic Differential Equations (FBSDEs), and we derive the Master Equation from a version of the chain rule (Ito's formula) for functions over flows of probability measures. Finally, we give a new form to the extension of MFGs to the case of major and minor players and, at least in the finite state space case, we describe an application to virus contagion (e.g. cyber security).

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