The Role of Alliances Scale in Public Goods Game with Alliance Strategy

In previous studies, alliance behavior has been shown to be effective in promoting and maintaining cooperation, and this has also been observed in real human societies. At the same time, there are many organizations and alliances of different sizes in reality due to the causes and evolution of alliances. Therefore, we investigate the effect of different alliance sizes on the evolution of cooperation in spatial public goods games with alliance strategies. The results show that expansion of alliance size does not always promote cooperation, although expansion of alliance size is beneficial to the spread of surviving alliance islands or clusters. Considering the formation and expansion of alliance clusters, there exists an optimal alliance scale that can promote and maintain cooperation most effectively. This is because, on the one hand, the size of the alliance is too small, and the aid within the alliance is too small to resist the invasion of defectors. On the other hand, with the expansion of alliance scale, the possibility that the funds raised by the alliance will be subsidized to the most likely alliance cluster will decrease, and the difficulty of maintaining cooperation will become greater.