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