Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hotelling Games with Random Tolerance Intervals   The classical Hotelling game is played on a line segment whose points
represent uniformly distributed clients. The $n$ players of the game are
servers who need to place themselves on the line segment, and once this is
done, each client gets served by the player closest to it. The goal of each
player is to choose its location so as to maximize the number of clients it
attracts.
  In this paper we study a variant of the Hotelling game where each client $v$
has a tolerance interval, randomly distributed according to some density
function $f$, and $v$ gets served by the nearest among the players eligible for
it, namely, those that fall within its interval. (If no such player exists,
then $v$ abstains.) It turns out that this modification significantly changes
the behavior of the game and its states of equilibria. In particular, it may
serve to explain why players sometimes prefer to "spread out", rather than to
cluster together as dictated by the classical Hotelling game.
  We consider two variants of the game: symmetric games, where clients have the
same tolerance range to their left and right, and asymmetric games, where the
left and right ranges of each client are determined independently of each
other. We fully characterize the Nash equilibria of the 2-player game. For at
least 3 players, we characterize a specific class of strategy profiles,
referred to as canonical profiles, and show that these profiles are the only
ones that may yield Nash equilibria in our game. Moreover, the canonical
profile, if exists, is uniquely defined for every $n$ and $f$. In both the
symmetric and asymmetric setting, we give necessary and sufficient conditions
for the canonical profile to be a Nash equilibrium, and demonstrate their
application for several distributions.

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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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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: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph