Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computing Nash Equilibria: Approximation and Smoothed Complexity   We show that the BIMATRIX game does not have a fully polynomial-time
approximation scheme, unless PPAD is in P. In other words, no algorithm with
time polynomial in n and 1/\epsilon can compute an \epsilon-approximate Nash
equilibrium of an n by nbimatrix game, unless PPAD is in P. Instrumental to our
proof, we introduce a new discrete fixed-point problem on a high-dimensional
cube with a constant side-length, such as on an n-dimensional cube with
side-length 7, and show that they are PPAD-complete. Furthermore, we prove,
unless PPAD is in RP, that the smoothed complexity of the Lemke-Howson
algorithm or any algorithm for computing a Nash equilibrium of a bimatrix game
is polynomial in n and 1/\sigma under perturbations with magnitude \sigma. Our
result answers a major open question in the smoothed analysis of algorithms and
the approximation of Nash equilibria.

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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga