The lecture, a continuation of last year's, continues the presentation of a new theory called " mean-field games theory ", developed in collaboration with Mr. Jean-Michel Lasry. The aim of this theory is to introduce, justify, analyze and apply in different contexts a new class of mathematical models for studying the collective behavior of a very large number of interacting agents (or players in the sense of game theory), all of whom wish to " optimize " their decisions.
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This year, we have completed the detailed presentation of the mathematical framework required to (rigorously) justify the limit when the number of players N tends towards infinity. On the one hand, we indicated the methods for solving non-linear PDEs posed on the space of probability measures, and on the other, we explained how this mathematical framework allowed us to rigorously deduce the equations and systems of " mean-field games " from the systems of equations corresponding to N-player Nash equilibria.