This paper investigates the critical role of trust and fatigue in human-cobot collaborative order picking, framing the challenge within the scope of Logistics 5.0: the implementation of human-robot symbiosis in smart logistics. We propose a dynamic, leader-follower Stackelberg game to model this interaction, where utility functions explicitly account for human fatigue and trust. Through agent-based simulations, we demonstrate that while a naive model leads to a "trust death spiral," a refined trust model creates a "trust synergy cycle," increasing productivity by nearly 100 percent. Finally, we show that a cobot operating in a Trust-Recovery Mode can overcome system brittleness after a disruption, reducing trust recovery time by over 75 percent compared to a non-adaptive model. Our findings provide a framework for designing intelligent cobot behaviors that fulfill the Industry 5.0 pillars of human-centricity, sustainability, and resilience.

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