RESUMO
We consider an evolutionary prisoner's dilemma on a random network. We introduce a simple quantitative network-based parameter and show that it effectively predicts the success of cooperation in simulations on the network. The criterion is shown to be accurate on a variety of networks with degree distributions ranging from regular to Poisson to scale free. The parameter allows for comparisons of random networks regardless of their underlying topology. Finally, we draw analogies between the criterion for the success of cooperation introduced here and existing criteria in other contexts.
Assuntos
Teoria dos Jogos , Algoritmos , Altruísmo , Evolução Biológica , Biofísica/métodos , Simulação por Computador , Comportamento Cooperativo , Humanos , Relações Interpessoais , Modelos Biológicos , Modelos Estatísticos , Distribuição de Poisson , Reprodutibilidade dos TestesRESUMO
We study the effects of degree-degree correlations on the success of cooperation in an evolutionary prisoner's dilemma played on a random network. When degree-degree correlations are not present, the standardized variance of the network's degree distribution has been shown to be an accurate analytical measure of network heterogeneity that can be used to predict the success of cooperation. In this paper, we use a local-mechanism interpretation of standardized variance to give a generalization to graphs with degree-degree correlations. Two distinct mechanisms are shown to influence cooperation levels on these types of networks. The first is an intrinsic measurement of base-line heterogeneity coming from the network's degree distribution. The second is the increase in heterogeneity coming from the degree-degree correlations present in the network. A strong linear relationship is found between these two parameters and the average cooperation level in an evolutionary prisoner's dilemma on a network.
RESUMO
We use the standardized variance (nu_{st}) of the degree distribution of a random network as an analytic measure of its heterogeneity. We show that nu_{st} accurately predicts, quantitatively, the success of cooperators in an evolutionary prisoner's dilemma. Moreover, we show how the generating functional expression for nu_{st} suggests an intrinsic interpretation for the heterogeneity of the network that helps explain local mechanisms through which cooperators thrive in heterogeneous populations. Finally, we give a simple relationship between nu_{st} , the cooperation level, and the epidemic threshold of a random network that reveals an appealing connection between epidemic disease models and the evolutionary prisoner's dilemma.
