Evolutionary Game in a Single Hub Structure

In this paper, we investigate the evolutionary game theory on a simplest heterogeneous network-a single hub structure. In order to describe the dynamics on structured populations, we firstly give a general form of a spatial replicator equation. Then according to it, the evolutionary equations describing the evolution of two strategies (cooperation and defection) are derived explicitly and the dynamics of the system is discussed theoretically and numerically. We found if judging the strategy according to its ability to resist the invasion of another, the cooperation does better than the defection. In some parameters when the population N is small, an initial D-hub system may evolve to an allcooperator (AllC) state. All of these phenomena can be well explained by corresponding replicator equation.