Structural Heterogeneity and Evolutionary Dynamics on Complex Networks

The study of evolutionary games on networks has revealed the impact of population structure on evolutionary dynamics. Unlike the case in well-mixed population where defection is favored by natural selection, certain types of networks have shown to favor cooperation. However, most previous research work has been focusing on frequency-based analysis, and emphasized on the update strategy adopted by each player, and thus generally considered the group of players with the same strategy as a whole. While it is powerful in deriving analytic results using this approach, the heterogeneity of players within such groups is effectively overlooked. In this paper, we attempt to emphasize more on the heterogeneity of players that comes from the network structure in evolutionary dynamics. Particularly, the prestige of a player is represented by its centrality, and it is reflected in an adapted payoff function. We provide several viable centrality measures that can be calculated using the adjacency matrix of the network. The relation between different centrality measures of the invader and the fixation of cooperation is analyzed via computational simulations. Results show that in the proposed model, compared to other three centrality measures, invaders with maximum betweenness centrality have significant advantage in terms of the fixation probability of cooperation, in both scale-free and small-world networks.