Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An ergodic problem for Mean Field Games: qualitative properties and
  numerical simulations   This paper is devoted to some qualitative descriptions and some numerical
results for ergodic Mean Field Games systems which arise, e.g., in the
homogenization with a small noise limit. We shall consider either power type
potentials or logarithmic type ones. In both cases, we shall establish some
qualitative properties of the effective Hamiltonian $\bar H$ and of the
effective drift $\bar b$. In particular we shall provide two cases where the
effective system keeps/looses the Mean Field Games structure, namely where
$\nabla_P \bar H(P,\alpha)$ coincides or not with $\bar b(P, \alpha)$.
  On the other hand, we shall provide some numerical tests validating the
aforementioned qualitative properties of $\bar H$ and $\bar b$. In particular,
we provide a numerical estimate of the discrepancy $\nabla_P \bar
H(P,\alpha)-\bar b(P, \alpha)$.

14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn