Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear Quadratic Mean Field Games -- Part I: The Asymptotic Solvability
  Problem   This paper investigates the so-called asymptotic solvability problem in
linear quadratic (LQ) mean field games. The model has asymptotic solvability if
for all sufficiently large population sizes, the corresponding game has a set
of feedback Nash strategies subject to a mild regularity requirement. We
provide a necessary and sufficient condition and show that in this case the
solution converges to a mean field limit. This is accomplished by developing a
re-scaling method to derive a low dimensional ordinary differential equation
(ODE) system, where a non-symmetric Riccati ODE has a central role.

16
The categories of this paper are: stat
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg