Coevolution of Structure and Strategy Promoting Fairness in the Ultimatum Game

We try to figure out how the structure evolution and strategy evolution commonly affect the emergence of fair behaviors in the ultimatum game under a complex network framework. By allowing the players to change their neighbors in the network as well as their strategies, several experiments have been conducted. Results of the simulations show that the coevolution has substantial impacts on the resulting outcomes for the strategy adopted as well as the ultimate structure. With increasing structure updating rate, players offer more in the ultimatum game, but players will offer less with increasing strategy updating rate. In particular, the ratio of structure updating to strategy updating also affects the emergence of fairness substantially because the larger the ratio, the more the players offer. In addition, the mutation in strategies plays a promoting role in the emergence of fairness. Moreover, the initial random network is evolved into the structure with small-world effects. By comparison with the traditional models of static structures, we show that allowing the network structure and strategy to coevolve generally promotes the emergence of fairness.