Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounds for the Nakamura number   The Nakamura number is an appropriate invariant of a simple game to study the
existence of social equilibria and the possibility of cycles. For symmetric
quota games its number can be obtained by an easy formula. For some subclasses
of simple games the corresponding Nakamura number has also been characterized.
However, in general, not much is known about lower and upper bounds depending
of invariants on simple, complete or weighted games. Here, we survey such
results and highlight connections with other game theoretic concepts.

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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th