Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear quadratic mean field social optimization: Asymptotic solvability
  and decentralized control   This paper studies asymptotic solvability of a linear quadratic (LQ) mean
field social optimization problem with controlled diffusions and indefinite
state and control weights. Starting with an $N$-agent model, we employ a
rescaling approach to derive a low-dimensional Riccati ordinary differential
equation (ODE) system, which characterizes a necessary and sufficient condition
for asymptotic solvability. The decentralized control obtained from the mean
field limit ensures a bounded optimality loss in minimizing the social cost
having magnitude $O(N)$, which implies an optimality loss of $O(1/N)$ per
agent. We further quantify the efficiency gain of the social optimum with
respect to the solution of the mean field game.

28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: econ
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph