Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimax Approach to First-Order Mean Field Games   The paper is devoted to the first-order mean field game system in the case
when the distribution of players can contain atoms. The proposed definition of
a generalized solution is based on the minimax approach to the Hamilton-Jacobi
equation. We prove the existence of the generalized (minimax) solution of the
mean filed game system using the Nash equilibrium in the auxiliary differential
game with infinitely many identical players. We show that the minimax solution
of the original system provide the $\varepsilon$-Nash equilibrium in the
differential game with finite number of players.

26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
9
The categories of this paper are: nlin