Human behavioral decision-making influences the gaming environment. In turn, changes in the gaming environmental impact individual strategic choices. However, there is scant exploration into how human behavioral decision-making coevolves with dilemma strength. Here, we propose a coevolutionary game model based on collective-risk social dilemma, where an increase in cooperators within the game group reduces the dilemma strength, and vice versa. Upon examining this coupled system, we find that the system is capable of achieving a relatively optimal state, wherein the population sustains a high level of cooperation and the dilemma strength remains at the lowest level. In addition, we have identified the conditions for the emergence of tristability and bistability in the coupled system and numerically validated our theoretical results. Furthermore, we find that the incorporation of institutional rewards not only promotes the appearance of the system's optimal state, where all individuals choose to cooperate and the dilemma strength is at its lowest level, but it also effectively averts the manifestation of the system's worst state, where all individuals resort to defection and the dilemma strength reaches its highest level. These findings illuminate how cooperation can be sustained when a dynamical coupling exists between individual decision-making and dilemma strength. Published by the American Physical Society 2024

Trust game is commonly used to study the evolution of trust among unrelated individuals. It offers valuable insights into human interactions in a range of disciplines, including economics, sociology and psychology. Previous research has revealed that reward and punishment systems can effectively promote the evolution of trust. However, these investigations overlook the gaming environment, leaving unresolved the optimal conditions for employing distinct incentives to effectively facilitate trust level. To bridge this gap, we introduce a transformation incentive mechanism in an N -player trust game, where trustees are given different forms of incentives depending on the number of trustees in the group. Using the Markov decision process approach, our research shows that as incentives increase, the level of trust rises continuously, eventually reaching a high level of coexistence between investors and trustworthy trustees. Specifically, in the case of smaller incentives, rewarding trustworthy trustees is more effective. Conversely, in the case of larger incentives, punishing untrustworthy trustees is more effective. Additionally, we find that moderate incentives have a positive impact on increasing the average payoff within the group.

In contemporary society, the effective utilization of public resources remains a subject of significant concern. A common issue arises from defectors seeking to obtain an excessive share of these resources for personal gain, potentially leading to resource depletion. To mitigate this tragedy and ensure sustainable development of resources, implementing mechanisms to either reward those who adhere to distribution rules or penalize those who do not, appears advantageous. We introduce two models: a tax-reward model and a tax-punishment model, to address this issue. Our analysis reveals that in the tax-reward model, the evolutionary trajectory of the system is influenced not only by the tax revenue collected but also by the natural growth rate of the resources. Conversely, the tax-punishment model exhibits distinct characteristics when compared with the tax-reward model, notably the potential for bistability. In such scenarios, the selection of initial conditions is critical, as it can determine the system’s path. Furthermore, our study identifies instances where the system lacks stable points, exemplified by a limit cycle phenomenon, underscoring the complexity and dynamism inherent in managing public resources using these models.

Trust plays a crucial role in social and economic interactions, serving as the foundation for social stability and human cooperation. Previous studies have explored the evolution of trust between investors and trustees by constructing trust game models, incorporating factors such as network structure, reputation, and incentives. However, these studies often assume that investors consistently maintain their investment behavior, neglecting the potential influence of the investment environment on investment behavior. To address this gap, we introduce a loss assessment mechanism and construct a trust game model. Specifically, investors first allocate their investment amount to an assessment agency, which divides the amount into two parts according to a certain allocation ratio. One part is used for investment assessment, and the results are fed back to the investors. If the payoff from this portion exceeds the investors’ expected value, the remaining amount is invested; otherwise, it is returned to the investors. The results indicate that investors with moderate expectations are more likely to form alliances with trustworthy trustees, thereby effectively promoting the evolution of trust. Conversely, lower or higher expectations yield opposite results. Additionally, we find that as investors’ expected values increase, the corresponding allocation ratio should also increase to achieve higher payoffs.