Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Greediness and Equilibrium in Congestion Games   Rosenthal (1973) introduced the class of congestion games and proved that
they always possess a Nash equilibrium in pure strategies. Fotakis et al.
(2005) introduce the notion of a greedy strategy tuple, where players
sequentially and irrevocably choose a strategy that is a best response to the
choice of strategies by former players. Whereas the former solution concept is
driven by strong assumptions on the rationality of the players and the common
knowledge thereof, the latter assumes very little rationality on the players'
behavior. From Fotakis \cite{fotakis10} it follows that for Tree Representable
congestion Games greedy behavior leads to a NE. In this paper we obtain
necessary and sufficient conditions for the equivalence of these two solution
concepts. Such equivalence enhances the viability of these concepts as
realistic outcomes of the environment. The conditions for such equivalence to
emerge for monotone symmetric games is that the strategy set has a tree-form,
or equivalently is a `extension-parallel graph'.

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The categories of this paper are: adap-org
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc