Abstract
Evolutionary graph theory studies evolutionary dynamics of a population which interactions are constrained by a graph structure. The replicator equation is one of the fundamental tools to study frequency-dependent selection in absence of mutations, this work provides the replicator equation for a specific family of graphs, characterized by connected degree-regular communities, using the method of pair approximation. The evolution of cooperation on such graphs is presented as an application of the proposed equation, showing that cooperation is sustainable for given conditions on the connectivity of the graph and on the cooperation cost.
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The loose wording is because it can’t be said that each DHVS spans a connected regular subgraph, given that in the span(DHVS) there are all the vertices in DHVS and all the vertices connected with these. Given that some of these vertices are frontier vertices (by definition), some of their neighbours have a different degree than the rest of vertices in the DHVS (hence the subgraph would not be regular).
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Cassese, D. (2018). Replicator Equation and the Evolution of Cooperation on Regular Communities. In: Cherifi, C., Cherifi, H., Karsai, M., Musolesi, M. (eds) Complex Networks & Their Applications VI. COMPLEX NETWORKS 2017. Studies in Computational Intelligence, vol 689. Springer, Cham. https://doi.org/10.1007/978-3-319-72150-7_70
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DOI: https://doi.org/10.1007/978-3-319-72150-7_70
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