Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence and Hardness of Strategic Schelling Segregation   The phenomenon of residential segregation was captured by Schelling's famous
segregation model where two types of agents are placed on a grid and an agent
is content with her location if the fraction of her neighbors which have the
same type as her is at least $\tau$, for some $0<\tau<1$. Discontent agents
simply swap their location with a randomly chosen other discontent agent or
jump to a random empty cell.
  We analyze a generalized game-theoretic model of Schelling segregation which
allows more than two agent types and more general underlying graphs modeling
the residential area. For this we show that both aspects heavily influence the
dynamic properties and the tractability of finding an optimal placement. We map
the boundary of when improving response dynamics (IRD), i.e., the natural
approach for finding equilibrium states, are guaranteed to converge. For this
we prove several sharp threshold results where guaranteed IRD convergence
suddenly turns into the strongest possible non-convergence result: a violation
of weak acyclicity. In particular, we show such threshold results also for
Schelling's original model, which is in contrast to the standard assumption in
many empirical papers. Furthermore, we show that in case of convergence, IRD
find an equilibrium in $\mathcal{O}(m)$ steps, where $m$ is the number of edges
in the underlying graph and show that this bound is met in empirical
simulations starting from random initial agent placements.

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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
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The categories of this paper are: eess
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: math
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th