Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long-range prisoner's dilemma game on a cycle   We investigate evolutionary dynamics of altruism with long-range interaction
on a cycle. The interaction between individuals is described by a simplified
version of the prisoner's dilemma (PD) game in which the payoffs are
parameterized by $c$, the cost of a cooperative action. In our model, the
probabilities of the game interaction and competition decay algebraically with
$r_{AB}$, the distance between two players $A$ and $B$, but with different
exponents: That is, the probability to play the PD game is proportional to
$r_{AB}^{-\alpha}$. If player $A$ is chosen for death, on the other hand, the
probability for $B$ to occupy the empty site is proportional to
$r_{AB}^{-\beta}$. In a limiting case of $\beta\to\infty$, where the
competition for an empty site occurs between its nearest neighbors only, we
analytically find the condition for the proliferation of altruism in terms of
$c_{th}$, a threshold of $c$ below which altruism prevails. For finite $\beta$,
we conjecture a formula for $c_{th}$ as a function of $\alpha$ and $\beta$. We
also propose a numerical method to locate $c_{th}$, according to which we
observe excellent agreement with the conjecture even when the selection
strength is of considerable magnitude.

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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph