Co-evolutionary dynamics of asymmetric <i>N</i> -player trust game with margin-driven environmental feedback

Current research on trust game (TG) has revealed the interplay between individual strategies and external incentive mechanisms. However, how individual decisions are influenced by environmental factors and how dynamic incentive mechanisms can promote the evolution of trust remain open questions. In this paper, we use a dynamic margin mechanism to characterize environmental dynamics and establish the co-evolutionary dynamics of an asymmetric N-player TG with dynamic margins. The model consists of two components: the dynamics of the asymmetric N-player TG and the evolution of the margin coefficient. The former describes the trust dynamics between investors and trustees, while the latter represents the dynamic adjustment of the margin based on different combinations of strategies. We analyze the existence and stability of possible fixed points in the system dynamics and reveal the critical role of dynamic margins in shaping the evolutionary process. Furthermore, we introduce a penalty mechanism for non-investors and find that under specific conditions, an appropriate penalty can induce persistent oscillations in the system, thereby influencing the evolution of trust. Finally, numerical simulations further validate the theoretical analysis. In general, this work explores the role of dynamic margins in fostering collective trust from an environmental feedback perspective, providing new insights into the evolution of trust in complex social interactions.