Among unrelated individuals, the emergence and maintenance of trust has always been a pressing issue to address, one that has garnered considerable attention through the framework provided by trust games. However, few studies have considered the effects of time delay in trust games. Given that decision-makers in trust games inherently exhibit lagged responses when observing the market, we explore the potential effects of time delay on the evolution of trust and develop an N-player trust game model based on investment behavior with time-delayed expected returns. We note that the system exhibits a stable interior equilibrium point, implying that investors and trustworthy trustees can coexist stably in the population, when the time delay is relatively small. Conversely, when the time delay is moderately large, the system exhibits a stable limit cycle, where the proportion in the population show oscillatory dynamics. Furthermore, we analyze the system's Hopf bifurcation points, identifying all critical thresholds responsible for inducing transitions under various conditions. The above theoretical results have been validated by numerical simulations.

中文翻译：

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时滞对不同投资行为的 N 人信任博弈演化动力学的影响


在不相关的个体中，信任的出现和维护一直是一个亟待解决的问题，通过信任游戏提供的框架，这个问题已经引起了相当大的关注。然而，很少有研究考虑信任游戏中时间延迟的影响。鉴于信任游戏中的决策者在观察市场时天生就表现出滞后反应，我们探讨了时间延迟对信任演变的潜在影响，并开发了一个基于具有时间延迟预期回报的投资行为的 N 人信任游戏模型。我们注意到，该系统表现出稳定的内部均衡点，这意味着当时间延迟相对较小时，投资者和值得信赖的受托人可以在人群中稳定共存。相反，当时间延迟适中时，系统表现出稳定的极限周期，其中总体中的比例表现出振荡动力学。此外，我们分析了系统的 Hopf 分叉点，确定了在各种条件下负责诱导转换的所有关键阈值。上述理论结果已通过数值模拟得到验证。