Reputation-based nonlinear investment promotes cooperation in networked N-player trust games

Trust underpins large-scale cooperation, yet it remains fragile among self-interested individuals. Trust games provide a classic framework for studying the evolutionary dynamics of trustworthy and untrustworthy behaviors under asymmetric payoff structures. However, in most existing trust-game models, investment rules are based on equal or linear allocation, failing to incentivize and constrain the behaviors of trustees effectively. To address this gap, we propose a reputation-based investment allocation mechanism in a networked N-player trust game. In this framework, individual behavior shapes reputation, reputation regulates investment allocation through a nonlinear softmax rule, and both payoff and reputation jointly influence strategy evolution, thereby forming a feedback loop. Numerical simulations demonstrate that this mechanism effectively directs resources toward high-reputation trustees, suppresses untrustworthy behavior, and improves both role-based cooperation index and the average payoff. Reputation-based nonlinear allocation is the key component, which converts reputation differences into resource-allocation advantages. A suitable balance between investment sensitivity and reputation preference is required: excessive reputation preference may reduce investor proportions and limit wealth generation. Thus, the optimal reputation preference is one that suppresses untrustworthy behavior while preserving enough investors to sustain capital flow. Tests on regular lattice, small-world, and scale-free networks show that the mechanism is not limited to the lattice, although stationary payoffs remain network-dependent. This study proposes a novel incentive framework in which reputation scoring, nonlinear allocation, payoff generation, and strategy updating are coupled into a feedback loop that sustains trust in networked N-player trust games.