Effects of social diversity on the evolutionary game and opinion dynamics

We study the role of social diversity in the evolutionary game and opinion dynamics on scale-free networks. Each individual is assigned a weight that is proportional to the power of its degree, where the exponent α is an adjustable parameter that controls the level of diversity among individuals in the network. It is found that there exists an optimal value of α, leading to the highest cooperation level or the fastest consensus. We give some qualitative explanations for the emergence of optimal α.