Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximate Equilibrium Computation for Discrete-Time Linear-Quadratic
  Mean-Field Games   While the topic of mean-field games (MFGs) has a relatively long history,
heretofore there has been limited work concerning algorithms for the
computation of equilibrium control policies. In this paper, we develop a
computable policy iteration algorithm for approximating the mean-field
equilibrium in linear-quadratic MFGs with discounted cost. Given the
mean-field, each agent faces a linear-quadratic tracking problem, the solution
of which involves a dynamical system evolving in retrograde time. This makes
the development of forward-in-time algorithm updates challenging. By
identifying a structural property of the mean-field update operator, namely
that it preserves sequences of a particular form, we develop a forward-in-time
equilibrium computation algorithm. Bounds that quantify the accuracy of the
computed mean-field equilibrium as a function of the algorithm's stopping
condition are provided. The optimality of the computed equilibrium is validated
numerically. In contrast to the most recent/concurrent results, our algorithm
appears to be the first to study infinite-horizon MFGs with non-stationary
mean-field equilibria, though with focus on the linear quadratic setting.

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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph