Evolutionary dynamics with the second-order reputation in the networked N-player trust game

Network science has become an emerging and promising discipline within academia, which has induced extensive concern from a diverse range of realms including economics, social and computer science, mathematics and statistical mechanics. In this work, we investigate the impact of network topology on an N-player trust game by considering the second-order reputation rule. The model consists of three types of participants: investors (trusters), trustworthy trustees, and untrustworthy trustees. Based on the underlying network topology, players will interact with their neighbors at each game round. At the end of each interaction, they will update their strategies concerning their individual payoff and reputation. Meanwhile, we use different social networks and temptations of defection to explore the effect of degree distribution and clustering coefficients on the cooperative behaviors. Besides, the steady state of systems can be arrived at through the detailed theoretical analyses, and then the evolutionary process is extensively simulated on some real-world networks. We find that the trust can be spread in different network topologies and the cooperation or trust can be maintained at the higher level even though the intensity of the dilemma is higher. In addition, under the same network structure, the higher the average degree distribution of the network, the higher the trust level; under the same average degree distribution, the higher the aggregation coefficient, the lower the trust level. Current results provide some new insights into the evolution of cooperation or trust within the structured populations.