Synergy Over Spiral: A Logistics 5.0 Game-Theoretic Model for Trust-Fatigue Co-regulation in Human-Cobot Order Picking

Soumyadeep Dhar; Ariyan Kumar Saha

cs.MAAug 5, 2025

Synergy Over Spiral: A Logistics 5.0 Game-Theoretic Model for Trust-Fatigue Co-regulation in Human-Cobot Order Picking

Authors: Soumyadeep Dhar, Ariyan Kumar Saha

Organizations: Department of Industrial and Systems Engineering, Indian Institute of Technology (IIT), Kharagpur, 721302, West Bengal, India. · Department of Computer Science and Engineering, RV College of Engineering, Bengaluru, 560059, Bengaluru, India.

Abstract

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.

Figures & tables

Parameter	Value	Description
$F_{thresh}$	80.0	Ergonomic fatigue threshold
$T_{0}$	0.5	Initial trust level
$\Delta T_{gain}$	0.05	Trust gain on success
$\Delta T_{loss}$	0.10	Trust loss on minor failure
$\Delta T_{severe}$	0.50	Trust loss on severe failure
Disruption Chance	0.10	Probability of a random event

Table 1: Key Simulation Parameters

Panel of Figure 1 — Figure 1: Experiment 1 Results: The contrast between the Naive and Refined Trust models.

Panel of Figure 2 — Figure 2: Experiment 2 Results: System resilience with and without the Apology Mechanism.

Model Version	Productivity	Final Fatigue	Final Trust	Trust Behavior / Recovery
v1.0 (Naive)	50	$\approx$ 50.0	0.00	Trust collapses (”Death Spiral”)
v1.1 (Refined)	98	$\approx$ 50.0	$\approx$ 1.00	Stable at maximum (”Synergy Cycle”)
v1.2 (Brittleness)	50	87.5	0.60	No recovery after severe failure
v1.3 (Resilience)	50	72.5	0.95	Fast recovery after severe failure

Table 2: Summary of Key Performance Indicators Across All Model Versions

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Abstract

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