Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spatial Evolutionary Games with small selection coefficients   Here we will use results of Cox, Durrett, and Perkins for voter model
perturbations to study spatial evolutionary games on $Z^d$, $d\ge 3$ when the
interaction kernel is finite range, symmetric, and has covariance matrix
$\sigma^2I$. The games we consider have payoff matrices of the form ${\bf 1} +
wG$ where ${\bf 1}$ is matrix of all 1's and $w$ is small and positive. Since
our population size $N=\infty$, we call our selection small rather than weak
which usually means $w =O(1/N)$.
  The key to studying these games is the fact that when the dynamics are
suitably rescaled in space and time they convergence to solutions of a reaction
diffusion equation (RDE). Inspired by work of Ohtsuki and Nowak and Tarnita et
al we show that the reaction term is the replicator equation for a modified
game matrix and the modifications of the game matrix depend on the interaction
kernel only through the values of two or three simple probabilities for an
associated coalescing random walk.
  Two strategy games lead to an RDE with a cubic nonlinearity, so we can
describe the phase diagram completely. Three strategy games lead to a pair of
coupled RDE, but using an idea from our earlier work, we are able to show that
if there is a repelling function for the replicator equation for the modified
game, then there is coexistence in the spatial game when selection is small.
This enables us to prove coexistence in the spatial model in a wide variety of
examples where the replicator equation of the modified game has an attracting
equilibrium with all components positive. Using this result we are able to
analyze the behavior of four evolutionary games that have recently been used in
cancer modeling.

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The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph