Integrating agent-based modeling and game theory for optimal water resource allocation within complex hierarchical systems

Effective water resource management in hierarchical systems is challenged by competing stakeholder interests, imperfect rationality, legislative constraints, varying hydrological conditions, and economic pressures. Traditional methods, such as agent-based models (ABM) and game theory (GT), have been applied separately to allocation problems but often fail to capture the dynamics of partial cooperation among stakeholders. This study addresses this gap by presenting a novel framework that integrates ABM and GT techniques-including the Shapley value (SV), least core (LC), weak least core (WLC), and proportional least core (PLC)-for conflict resolution and optimal water allocation. The integrated ABM-GT framework simulates real-world scenarios by modeling the dynamics of partial cooperation, where agents iteratively adjust their resource contributions over time based on outcomes. The ABM component captures the adaptive behaviors of agents, while the GT component provides mechanisms for the fair allocation of benefits. The framework is applied to a case study of the Roodbal basin in Fars province, Iran, which comprises four agricultural zones facing significant water management challenges due to droughts and legislative constraints. Results from a 15-year simulation demonstrate that the ABM-GT framework enhances stakeholder cooperation and responsiveness. Partial cooperation among farmer agents led to an increase in net benefits by up to 150% compared to non-cooperative scenarios during dry years, with the maximum net benefit reaching $211.53 million using the PLC method. Agents with higher economic potential were more responsive to incentives, while those with lower economic potential increased their cooperation in response to water shortages. Specifically, the overall average contribution to the coalition increased from 36% to 52% for zones 3 and 4 during periods of water scarcity.