Higher-order interactions and zero-determinant strategies in the public goods game

Since the ingenious discovery of zero-determinant (ZD) strategies by Press and Dyson, many efforts have been devoted to the evolutionary performance of ZD strategies. Recently, the effects of higher-order interactions on evolutionary games have attracted widespread interests, whereas it remains unknown how higher-order interactions affect the evolutionary performance of ZD strategies. This paper focuses on the role of higher-order interactions on evolutionary ZD strategies in iterated public goods game, where the baseline payoff is a key parameter to describe nodes’ extent of reciprocity in both first-order and second-order interactions. Through the adaptive-like dynamics, we found that there is a critical value of each network, above which the networked game will converge to a consensus state where all the nodes obtain the same payoff. This critical value is significantly affected by the relative strength of higher-order interactions with a U-shaped trend. Numerical simulations are carried out to explore how the network structures affect the dynamics. The results in networks with different sizes indicate that networks with higher average degree are more easily to converge to the consensus state. The simulations on a real-world network further support the theoretical conclusions.