An evolutionary trust game model with group reputation within the asymmetric population

Trust plays a pivotal role in the evolution of human societies. In accordance with the classical trust game, an investor is required to make an investment, while the trustee has the option to be either trustworthy or untrustworthy. In this study, we differentiate between investors and trustees. Strategy imitation occurs only among individuals of the same type, and their proportions remain constant. Trustees can oscillate between being trustworthy and untrustworthy. Meanwhile, investors have the choice to either invest or abstain from investing. Using the replicator dynamics, we investigate the N-player trust game where the group reputation is introduced into the population of trustees. We discover that introducing the group reputation facilitates a stable state of co-existence between investing investors and trustworthy trustees. Moreover, it’s found that with the introduction of group reputation, a moderate increase in the reputation parameter can lead to a reduction in relative productivity of the prosocial strategies at optimal average payoff when there is full trust and investment within the group. The current work highlights the nuanced impact of group reputation on the dynamics of trust and investment, providing some new insights that could enhance cooperation and social welfare in various social contexts.