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A spatial model for selection and cooperation

Part of: Time-dependent statistical mechanics (dynamic and nonequilibrium) Special processes

Published online by Cambridge University Press:  22 June 2017

Peter Czuppon  and
Peter Pfaffelhuber
Peter Pfaffelhuber*
Affiliation:
University of Freiburg
*
** Postal address: Department of Mathematical Stochastics, University of Freiburg, 79104 Freiburg, Germany.
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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. A special choice of interaction kernels yield that for α > γ cooperators always die out, but if γ > α, cooperation is the winning strategy.

Keywords

Interacting particle systemvoter modelcooperationphase transitionextinctionclustering

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 82C22: Interacting particle systems 92D15: Problems related to evolution
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 2 , June 2017 , pp. 522 - 539
Copyright
Copyright © Applied Probability Trust 2017 

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