Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Efficient Approximation Algorithm for the Colonel Blotto Game   In the storied Colonel Blotto game, two colonels allocate $a$ and $b$ troops,
respectively, to $k$ distinct battlefields. A colonel wins a battle if they
assign more troops to that particular battle, and each colonel seeks to
maximize their total number of victories. Despite the problem's formulation in
1921, the first polynomial-time algorithm to compute Nash equilibrium (NE)
strategies for this game was discovered only quite recently. In 2016,
\citep{ahmadinejad_dehghani_hajiaghayi_lucier_mahini_seddighin_2019} formulated
a breakthrough algorithm to compute NE strategies for the Colonel Blotto
game\footnote{To the best of our knowledge, the algorithm from
\citep{ahmadinejad_dehghani_hajiaghayi_lucier_mahini_seddighin_2019} has
computational complexity $O(k^{14}\max\{a,b\}^{13})$}, receiving substantial
media coverage (e.g. \citep{Insider}, \citep{NSF}, \citep{ScienceDaily}).
  In this work, we present the first known $\epsilon$-approximation algorithm
to compute NE strategies in the two-player Colonel Blotto game in runtime
$\widetilde{O}(\epsilon^{-4} k^8 \max\{a,b\}^2)$ for arbitrary settings of
these parameters. Moreover, this algorithm computes approximate coarse
correlated equilibrium strategies in the multiplayer (continuous and discrete)
Colonel Blotto game (when there are $\ell > 2$ colonels) with runtime
$\widetilde{O}(\ell \epsilon^{-4} k^8 n^2 + \ell^2 \epsilon^{-2} k^3 n (n+k))$,
where $n$ is the maximum troop count. Before this work, no polynomial-time
algorithm was known to compute exact or approximate equilibrium (in any sense)
strategies for multiplayer Colonel Blotto with arbitrary parameters.
  Our algorithm computes these approximate equilibria by a novel (to the
author's knowledge) sampling technique with which we implicitly perform
multiplicative weights update over the exponentially many strategies available
to each player.

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The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg