Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fault-Tolerant Hotelling Games   The $n$-player Hotelling game calls for each player to choose a point on the
line segment, so as to maximize the size of his Voronoi cell. This paper
studies fault-tolerant versions of the Hotelling game. Two fault models are
studied: line faults and player faults. The first model assumes that the
environment is prone to failure: with some probability, a disconnection occurs
at a random point on the line, splitting it into two separate segments and
modifying each player's Voronoi cell accordingly. A complete characterization
of the Nash equilibria of this variant is provided for every $n$. Additionally,
a one to one correspondence is shown between equilibria of this variant and of
the Hotelling game with no faults. The second fault model assumes the players
are prone to failure: each player is removed from the game with i.i.d.
probability, changing the payoffs of the remaining players accordingly. It is
shown that for $n \geq 3$ this variant of the game has no Nash equilibria.

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The categories of this paper are: physics
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The categories of this paper are: chem-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: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: math