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.
Mots-clés : Mean field games, value multifucntion, viability property, set-valued derivative
@article{COCV_2020__26_1_A33_0,
author = {Averboukh, Yurii},
title = {Viability analysis of the first-order mean field games},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {26},
year = {2020},
doi = {10.1051/cocv/2019013},
mrnumber = {4088358},
zbl = {1437.91048},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2019013/}
}
TY - JOUR AU - Averboukh, Yurii TI - Viability analysis of the first-order mean field games JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2020 VL - 26 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2019013/ DO - 10.1051/cocv/2019013 LA - en ID - COCV_2020__26_1_A33_0 ER -
Averboukh, Yurii. Viability analysis of the first-order mean field games. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 33. doi : 10.1051/cocv/2019013. http://www.numdam.org/articles/10.1051/cocv/2019013/
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The research is supported by RFBR (grant N 17-01-00069).
