Effects of Some Topological Ingredients on the Evolutionary Ultimatum Game

This study aims at figuring out the crucial topological ingredients which affect the outcomes of the ultimatum game located on different networks, encompassing the regular network, the random network, the smallworld network, and the scale-free network. With the aid of random interchanging algorithm, we investigate the relations between the outcomes of the ultimatum game and some topological ingredients, including the average range, the clustering coefficient and the heterogeneity, and so forth. It is found that for the regular, random and small-work networks, the average range and the clustering coefficient have evident impacts on the ultimatum game, while for the scale-free network, the original degree heterogeneity and the underlying rich-club characterizations are the mainly important topological ingredients that influence the outcomes of ultimatum game substantially.