Evolution of cooperation on dynamical graphs

Ádám Kun, I. Scheuring

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

There are two key characteristic of animal and human societies: (1) degree heterogeneity, meaning that not all individual have the same number of associates; and (2) the interaction topology is not static, i.e. either individuals interact with different set of individuals at different times of their life, or at least they have different associations than their parents. Earlier works have shown that population structure is one of the mechanisms promoting cooperation. However, most studies had assumed that the interaction network can be described by a regular graph (homogeneous degree distribution). Recently there are an increasing number of studies employing degree heterogeneous graphs to model interaction topology. But mostly the interaction topology was assumed to be static. Here we investigate the fixation probability of the cooperator strategy in the prisoner's dilemma, when interaction network is a random regular graph, a random graph or a scale-free graph and the interaction network is allowed to change. We show that the fixation probability of the cooperator strategy is lower when the interaction topology is described by a dynamical graph compared to a static graph. Even a limited network dynamics significantly decreases the fixation probability of cooperation, an effect that is mitigated stronger by degree heterogeneous networks topology than by a degree homogeneous one. We have also found that from the considered graph topologies the decrease of fixation probabilities due to graph dynamics is the lowest on scale-free graphs.

Original languageEnglish
Pages (from-to)65-68
Number of pages4
JournalBioSystems
Volume96
Issue number1
DOIs
Publication statusPublished - Apr 2009

Fingerprint

Evolution of Cooperation
Topology
Fixation
Graph in graph theory
Interaction
Regular Graph
Random Graphs
Dynamic Graphs
Heterogeneous networks
Population Structure
Decrease
Prisoners' Dilemma
Network Dynamics
Heterogeneous Networks
Degree Distribution
Network Topology
Animals
Lowest
Population

Keywords

  • Fixation probability
  • Game theory
  • Prisoner's dilemma
  • Scale-free network

ASJC Scopus subject areas

  • Biochemistry, Genetics and Molecular Biology(all)
  • Applied Mathematics
  • Modelling and Simulation
  • Statistics and Probability

Cite this

Evolution of cooperation on dynamical graphs. / Kun, Ádám; Scheuring, I.

In: BioSystems, Vol. 96, No. 1, 04.2009, p. 65-68.

Research output: Contribution to journalArticle

Kun, Ádám ; Scheuring, I. / Evolution of cooperation on dynamical graphs. In: BioSystems. 2009 ; Vol. 96, No. 1. pp. 65-68.
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