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Seminario di equazioni differenziali e applicazioni: “Viability analysis of the first-order mean field games”

Giovedì 18 Aprile 2019, ore 12:00 - Aula 2BC60 - Yurii Averboukh

ARGOMENTI: Seminars

Giovedì 18 Aprile 2019 alle ore 12:00 in Aula 2BC60, Yurii Averboukh (Krasovskii Institute of Mathematics and Mechanics, Yekaterinburg, Russia) terrà un seminario dal titolo “Viability analysis of the first-order mean field games”.

Abstract
The talk is concerned with the dependence of the solution of the mean field game on the initial distribution of players. This dependence previously was described using the master equation proposed by Lions. However, the existence result for the master equation is proved either for the nondegenerate stochastic mean field games satisfying monotonicity conditions or for deterministic mean field games on the short time interval. In the talk the case of nonlinear deterministic mean field game is considered.
The main object of study is the mapping which assigns to the initial time and the initial distribution of players the set of expected rewards of the representative player corresponding to solutions of mean field game. This mapping can be regarded as a value multifunction. It is an extension of the value function studied within the approach involving the master equation. The main result is the sufficient condition for a multifunction to be a value multifunction. It states that if a multifunction is viable with respect to the dynamics generated by the original mean field game, then it is a value multifunction. Furthermore, the infinitesimal variant of this condition is derived. It is expressed in the terms of the set-valued derivative of the multivalued function by virtue of the mean field game dynamics.

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