Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiplicative weights, equalizers, and P=PPAD   We show that, by using multiplicative weights in a game-theoretic thought
experiment (and an important convexity result on the composition of
multiplicative weights with the relative entropy function), a symmetric
bimatrix game (that is, a bimatrix matrix wherein the payoff matrix of each
player is the transpose of the payoff matrix of the other) either has an
interior symmetric equilibrium or there is a pure strategy that is weakly
dominated by some mixed strategy. Weakly dominated pure strategies can be
detected and eliminated in polynomial time by solving a linear program.
Furthermore, interior symmetric equilibria are a special case of a more general
notion, namely, that of an "equalizer," which can also be computed efficiently
in polynomial time by solving a linear program. An elegant "symmetrization
method" of bimatrix games [Jurg et al., 1992] and the well-known
PPAD-completeness results on equilibrium computation in bimatrix games
[Daskalakis et al., 2009, Chen et al., 2009] imply then the compelling P =
PPAD.

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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: math
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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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: eess