Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coordination Games on Weighted Directed Graphs   We study strategic games on weighted directed graphs, in which the payoff of
a player is defined as the sum of the weights on the edges from players who
chose the same strategy, augmented by a fixed non-negative integer bonus for
picking a given strategy. These games capture the idea of coordination in the
absence of globally common strategies.
  We identify natural classes of graphs for which finite improvement or
coalition-improvement paths of polynomial length always exist, and, as a
consequence, a (pure) Nash equlibrium or a strong equilibrium can be found in
polynomial time.
  The considered classes of graphs are typical in network topologies: simple
cycles correspond to the token ring local area networks, while open chains of
simple cycles correspond to multiple independent rings topology from the
recommendation G.8032v2 on the Ethernet ring protection switching. For simple
cycles these results are optimal in the sense that without the imposed
conditions on the weights and bonuses a Nash equilibrium may not even exist.
  Finally, we prove that the problem of determining the existence of a Nash
equilibrium or of a strong equilibrium in these games is NP-complete already
for unweighted graphs and with no bonuses assumed. This implies that the same
problems for polymatrix games are strongly NP-hard.

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The categories of this paper are: alg-geom
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
2
The categories of this paper are: math
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph