Evolution of trust in a hierarchical population with different investors based on investment behavioral theory

The study of trust behavior between investors and trustees through trust games has been a hot topic recently. In previous research, the standard N−player trust game model has been used to reveal some aspects of trust evolution, but does not consider the risk perception of investors. According to behavioral investment theory, investors have different sensitivities to investment risk due to their individual environments and characteristics. Here, we construct an N-player trust game model where we divide investors into two categories, namely, venture investors and conservative investors. Conservative investors are willing to pay an information cost upfront to avoid investment risk, while venture investors are not. By analyzing replicator equations, we find that the system has an asymptotically stable internal equilibrium point when the group size is large, while when the group size is small, the system becomes a Hamiltonian system with a stable periodic solution. Our result shows that a lower information cost leads to a higher proportion of trustworthy trustees and thus reduces the portion of untrustworthy trustees.