Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Short time solution to the master equation of a first order mean field
  game system   The goal of this paper is to show existence of short-time classical solutions
to the so called Master Equation of \emph{first order} Mean Field Games, which
can be thought of as the limit of the corresponding master equation of a
stochastic mean field game as the individual noises approach zero. Despite
being the equation of an idealistic model, its study is justified as a way of
understanding mean field games in which the individual players'~randomness is
negligible; in this sense it can be compared to the study of ideal fluids
\cite{gangboberkeleynotes}. We restrict ourselves to potential mean field games
but do not impose any monotonicity conditions on the running and initial costs,
and we do not require convexity of the Hamiltonian, thus extending the result
of \cite{mfgmain} to a considerably broader class of Hamiltonians.

17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn