Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Totally Unimodular Congestion Games   We investigate a new class of congestion games, called Totally Unimodular
(TU) Congestion Games, where the players' strategies are binary vectors inside
polyhedra defined by totally unimodular constraint matrices. Network congestion
games belong to this class.
  In the symmetric case, when all players have the same strategy set, we design
an algorithm that finds an optimal aggregated strategy and then decomposes it
into the single players' strategies. This approach yields strongly
polynomial-time algorithms to (i) find a pure Nash equilibrium, and (ii)
compute a socially optimal state, if the delay functions are weakly convex. We
also show how this technique can be extended to matroid congestion games.
  We introduce some combinatorial TU congestion games, where the players'
strategies are matchings, vertex covers, edge covers, and stable sets of a
given bipartite graph. In the asymmetric case, we show that for these games (i)
it is PLS-complete to find a pure Nash equilibrium even in case of linear delay
functions, and (ii) it is NP-hard to compute a socially optimal state, even in
case of weakly convex delay functions.

5
The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
18
The categories of this paper are: econ
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The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: math
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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: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin