arXiv:2610.35997v1 Announce Type: new Abstract: One-person companies (OPCs) are emerging enterprises operated by individual entrepreneurs through digital platforms and LLM-based AI agents. These highly skilled entrepreneurs are characterized by being digital nomads, with limited reliance on local ecosystems. Governments in China use distinct regional support policies to attract mobile OPCs, turning local support into a cross-regional coordination problem. OPCs compare regions to maximize their own utility, but imperfect policy perceptions may cause them to reject otherwise suitable locations. Existing policy-learning methods optimize resources under fixed perceptions, while consensus-formation methods aggregate views without feeding cognitive changes back into policy learning. This disconnect produces mismatched location choices and inefficient regional policy adjustment. We introduce PolicyMediator, a cognition-constrained leader-multi-follower Stackelberg framework with bilateral mediation. The mediator explains verified policies to OPCs to build awareness and trust, and reports their needs and unresolved concerns to governments for policy learning. Its self-evolving skills retain, revise, or prune strategies using verification, allocation, capacity, and objective trajectories rather than mediation success alone. Across six-region simulations in China with five OPC types, five scenarios, and three OPC-simulator backbones, PolicyMediator ranks first in all 15 OPC-backbone--scenario combinations. Over the eight-baseline mean, it improves the aggregate government objective, combining economic performance, employment benefit, and policy-access equality, by 42.4% and average OPC utility by 40.9%.