A network growth model based on the evolutionary ultimatum game

In this paper, we provide a network growth model with incorporation into the ultimatum game dynamics. The network grows on the basis of the payoff-oriented preferential attachment mechanism, where a new node is added into the network and attached preferentially to nodes with higher payoffs. The interplay between the network growth and the game dynamics gives rise to quite interesting dynamical behaviors. Simulation results show the emergence of altruistic behaviors in the ultimatum game, which is affected by the growing network structure. Compared with the static counterpart case, the levels of altruistic behaviors are promoted. The corresponding strategy distributions and wealth distributions are also presented to further demonstrate the strategy evolutionary dynamics. Subsequently, we turn to the topological properties of the evolved network, by virtue of some statistics. The most studied characteristic path length and the clustering coefficient of the network are shown to indicate their small-world effect. Then the degree distributions are analyzed to clarify the interplay of structure and evolutionary dynamics. In particular, the difference between our growth network and the static counterpart is revealed. To explain clearly the evolved networks, the rich-club ordering and the assortative mixing coefficient are exploited to reveal the degree correlation.