${N}$-Player Trust Game With Second-Order Reputation Evaluation in the Networked Population

Trust has played a significant role in the maintenance of social links, which has attracted a great deal of concern from a diverse range of fields including economics, finance, and social science. In this article, we investigate the effect of second-order reputation evaluation on trust game dilemma and explore how individuals establish an indirect reciprocal relationship by adjusting their reputation. First, a novel ${N}$-player trust game is proposed by combining the payoff-driven and reputation-driven update processes. Second, four classical “second-order” norms are introduced to evaluate individual reputation, which will be judged by both their own strategies and the reputation status of their counterparts. Finally, through extensive simulations on different network topologies, we find that untrustworthy trustees would change their strategies with the help of a reputation signal. Meanwhile, the structured population presents a nonmonotonic cooperation trend with the increase of reputation strength in the mixed imitation process. Besides, there is an optimal interval that can promote the continuous emergence of trust between investors and trustworthy trustees. The current results are of high importance to understand the emergence of mutually beneficial symbiosis of biological groups inside an unknown environment.