Volume 26, 2020
|Number of page(s)||35|
|Published online||21 April 2020|
Viability analysis of the first-order mean field games*
Krasovskii Institute of Mathematics and Mechanics,
16, S. Kovalevskoi Str.,
2 Ural Federal University, 19 Mira Str., Yekaterinburg, Russia.
** Corresponding author: firstname.lastname@example.org
Accepted: 15 March 2019
In the paper, we examine the dependence of the solution of the deterministic mean field game on the initial distribution of players. 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. We obtain 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.
Mathematics Subject Classification: 91A10 / 91A23 / 49J52 / 49J53 / 46G05 / 49J21
Key words: Mean field games / value multifucntion / viability property / set-valued derivative
© EDP Sciences, SMAI 2020
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