Prisoner's dilemma game with heterogeneous influential effect on regular small-world networks

The effect of heterogeneous influence of different individuals oil the maintenance of co-operative behaviour is studied in an evolutionary Prisoner's Dilemma game with players located oil the sites of regular small-world networks. The players interacting with their neighbours call either co-operate or defect and update their states by choosing one of the neighbours and adopting its strategy with a probability depending on the payoff difference. The selection of the neighbour obeys a preferential rule: the more influential a neighbour, the larger the probability it is picked. It is found that this simple preferential selection rule can promote continuously the co-operation of the whole population with the strengthening of the disorder of the underlying network.