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arXiv · 1603.00645

A spatial model for selection and cooperation

Peter Czuppon·Peter Pfaffelhuber
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Abstract

We study the evolution of cooperation in an interacting particle system with two types. The model we investigate is an extension of a two-type biased voter model. One type (called defector) has a (positive) bias $α$ with respect to the other type (called cooperator). However, a cooperator helps a neighbor (either defector or cooperator) to reproduce at rate $γ$. We prove that the one-dimensional nearest-neighbor interacting dynamical system exhibits a phase transition at $α=γ$. For $α>γ$ cooperators always die out, but if $γ>α$, cooperation is the winning strategy.

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Peter Czuppon, Peter Pfaffelhuber. 2016-11-02. A spatial model for selection and cooperation. https://doi.org/10.1017/jpr.2017.15

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