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's theme concerns the case of finite state spaces for players, and the existence and uniqueness of regular solutions in this case.