| Abstract: |
| In order to use solutions of the mean field games PDE system to control solutions of N-player games as N goes to infinity, we must be able to take initial distributions which are the sum of Dirac masses. Relatedly, the natural space of data is probability measures. In a number of works (including those by the speaker), instead, subsets of the set of probability measures are used, such as probability measures induced by smooth functions. In this work, we instead take a larger space of data than probability measures, considering pseudomeasures as initial distributions. We give a class of nonseparable Hamiltonians for which we can prove existence of solutions of the mean field games PDE system with pseudomeasure initial data. This includes joint work with Milton Lopes Filho, Anna Mazzucato, and Helena Nussenzveig Lopes. |
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