Integrating opinion dynamics and differential game modeling for sustainable groundwater management

Groundwater overextraction presents persistent challenges due to strategic interdependence among decentralized users. While game-theoretic models have advanced the analysis of individual incentives and collective outcomes, most frameworks assume fully rational agents and neglect the role of cognitive and social factors. This study proposes a coupled model that integrates opinion dynamics with a differential game of groundwater extraction, capturing the interaction between institutional authority and evolving stakeholder preferences. Stakeholders form and adjust tax preferences through hierarchical social structures, which in turn influence extraction decisions. To validate theoretical predictions and simulation outcomes, we set key parameters using data from the Western La Mancha Aquifer in Spain. The analysis reveals that aquifer depletion induces a self-regulating mechanism through reduced taxes and withdrawals. However, weak social consensus raises governance costs by increasing uncertainty in compliance behavior. Simulation results further show that leader cohesion plays a key role in maintaining system-wide consensus, and that uniform tax instruments perform poorly under behavioral heterogeneity. The findings underscore the importance of bounded cognitive divergence, consistent leadership objectives, and structured communication in sustaining effective coordination. This framework offers a behaviorally grounded perspective on groundwater governance and lays the foundation for incorporating adaptive behavior and spatial heterogeneity in future research.