The Dynamics of Trust: A Stochastic Levy Model Capturing Sudden Behavioral Jumps

Trust is the invisible glue that holds together the fabric of societies, economic systems, and political institutions. Yet, its dynamics-especially in real-world settings remain unpredictable and difficult to control. While classical trust game models largely rely on discrete frameworks with limited noise, they fall short in capturing sudden behavioral shifts, extreme volatility, or abrupt breakdowns in cooperation.Here, we propose-for the first time a comprehensive stochastic model of trust based on L\'evy processes that integrates three fundamental components: Brownian motion (representing everyday fluctuations), Poissonian jump intensity (capturing the frequency of shocks), and random distributions for jump magnitudes. This framework surpasses conventional models by enabling simulations of phenomena such as "sudden trust collapse," "chaotic volatility," and "nonlinear recoveries" dynamics often neglected in both theoretical and empirical studies.By implementing four key simulation scenarios and conducting a detailed parameter sensitivity analysis via 3D and contour plots, we demonstrate that the proposed model is not only mathematically more advanced, but also offers a more realistic representation of human dynamics compared to previous approaches. Beyond its technical contributions, this study outlines a conceptual framework for understanding fragile, jump-driven behaviors in social, economic, and geopolitical systems-where trust is not merely a psychological construct, but an inherently unstable and stochastic variable best captured through L\'evy based modeling.