Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the long time convergence of potential MFG   We look at the long time behavior of potential Mean Field Games (briefly MFG)
using some standard tools from weak KAM theory. We first show that the
time-dependent minimization problem converges to an ergodic constant
$-\lambda$, then we provide a class of examples where the value of the
stationary MFG minimization problem is strictly greater than $-\lambda$. This
will imply that the trajectories of the time-dependent MFG system do not
converge to static equilibria.

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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an