Analyzing Multi-player Equalizer Strategy in Iterated Threshold Public Goods Game

In this paper, we investigate the multi-player equalizer strategy in the public goods game with threshold, a kind of key zero-determinant strategies in iterated games that can enforce opponents' long-term payoff to a fixed value. This paper studies the role of the equalizer strategy on the total amount of endowment in the particular scenario of the iterated multi-player game, where everyone will suffer a loss if the endowment does not exceed a threshold. Our results show that the threshold that the equalizer strategy can enforce to reach varies depending on the reward and risk factors. This also provides a potential clue on how humanity should reach a consensus to avoid the collective-risk social dilemma.