Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Territorial Raider Game and Graph Derangements   A derangement of a graph $G=(V,E)$ is an injective function $f:V\to V$ such
that for all $v\in V$, $f(v)\neq v$ and $(v,f(v))\in E$. Not all graphs admit a
derangement and previous results have characterized graphs with derangements
using neighborhood conditions for subsets of $V$. We establish an alternative
criterion for the existence of derangements on a graph. We analyze strict Nash
equilibria of the biologically motivated Territorial Raider Game, a
multi-player competition for resources in a spatially structured population
based on animal raiding and defending behavior. We find that a graph $G$ admits
a derangement if and only if there is a strict Nash equilibrium of the
Territorial Raider game on $G$.

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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: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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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-lat
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The categories of this paper are: patt-sol
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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: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int