The coevolutionary ultimatum game on different network topologies

In this paper, a model of ultimatum game is discussed from the coevolutionary perspective, where strategy dynamics and structure dynamics coexist. The interplay between structure dynamics and strategy dynamics leads to overwhelmingly interesting evolved topology and fairness behaviors. It is found that fair division emerges for specific ratios of structure updating probability to strategy updating probability. Furthermore, it is shown that the initial structures have no essentially different effect on the coevolutionary results. In particular, the results for strategy are almost similar whenever the initial structure is set to be the nearest-neighbor coupled network, the ER random network or the scale-free network. Besides, the effects of other spatial factors are also investigated, e.g. the population size has a positive influence on the offer, while the average degree has a negative effect. In addition, one extrinsic factor, the background payoff, is also of great importance in promoting fair divisions. Apart from above, we study the properties of the evolved networks, which have the small-world effect and positive assortative behaviors.