Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Tropical polyhedra are equivalent to mean payoff games
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg