Trust has played a pivotal role in the evolution of modern human societies, and it continues to be an essential underpinning of our social interactions. It is therefore important that we develop rigorous mathematical foundations that will enable us to better understand what promotes and what erodes trust and how to best preserve trustworthiness. To that effect we here propose a trust game, wherein investors, trustworthy trustees, and untrustworthy trustees compete for assets subject to a third-party evaluation system that oversees and modifies each individual reputation. We use Monte Carlo simulations on social networks to determine critical values of the degree of rationality and the reputation threshold that warrant high levels of trust and social wealth. We show that if investors have access to the reputation scores of trustees, the fraction of untrustworthy trustees drops if only the degree of rationality is sufficiently large, and this irrespective of the reputation threshold that determines the cutoff for untrustworthiness. But even though investors are allowed irrational investments, trust can still proliferate if the reputation threshold is sufficiently high. Our results thus formalize essential mechanisms of trust in social networks, which also outline policies to diminish untrustworthiness that can be employed in real life.

In the field of evolutionary game theory, network reciprocity has become an important means to promote the level of promotion within the population system. Recently, the interdependency provides a novel perspective to understand the widespread cooperation behavior in many real-world systems. In previous works, interdependency is often built from the direct or indirect connections between two networks through the one-to-one mapping mode. However, under many realistic scenarios, players may need much more information from many neighboring agents so as to make a more rational decision. Thus, beyond the one-to-one mapping mode, we investigate the cooperation behavior on two interdependent lattices, in which the utility evaluation of a focal player on one lattice may not only concern himself, but also integrate the payoff information of several corresponding players on the other lattice. Large quantities of simulations indicate that the cooperation can be substantially promoted when compared to the traditionally spatial lattices. The cluster formation and phase transition are also analyzed in order to explore the role of interdependent utility coupling in the collective cooperation. Current results are beneficial to deeply understand various mechanisms to foster the cooperation exhibited inside natural, social and engineering systems.