Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Necessary and sufficient condition for equilibrium of the Hotelling
  model   We study a model of vendors competing to sell a homogeneous product to
customers spread evenly along a linear city. This model is based on Hotelling's
celebrated paper in 1929. Our aim in this paper is to present a necessary and
sufficient condition for the equilibrium. This yields a representation for the
equilibrium. To achieve this, we first formulate the model mathematically.
Next, we prove that the condition holds if and only if vendors are equilibrium.

4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an