### 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 language | English |
---|---|

Pages (from-to) | 65-68 |

Number of pages | 4 |

Journal | BioSystems |

Volume | 96 |

Issue number | 1 |

DOIs | |

Publication status | Published - Apr 2009 |

### Fingerprint

### 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

*BioSystems*,

*96*(1), 65-68. https://doi.org/10.1016/j.biosystems.2008.11.009

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

Research output: Contribution to journal › Article

*BioSystems*, vol. 96, no. 1, pp. 65-68. https://doi.org/10.1016/j.biosystems.2008.11.009

}

TY - JOUR

T1 - Evolution of cooperation on dynamical graphs

AU - Kun, Ádám

AU - Scheuring, I.

PY - 2009/4

Y1 - 2009/4

N2 - 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.

AB - 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.

KW - Fixation probability

KW - Game theory

KW - Prisoner's dilemma

KW - Scale-free network

UR - http://www.scopus.com/inward/record.url?scp=61349121993&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=61349121993&partnerID=8YFLogxK

U2 - 10.1016/j.biosystems.2008.11.009

DO - 10.1016/j.biosystems.2008.11.009

M3 - Article

C2 - 19095039

AN - SCOPUS:61349121993

VL - 96

SP - 65

EP - 68

JO - BioSystems

JF - BioSystems

SN - 0303-2647

IS - 1

ER -