Bargaining for Water: An Integrated Nash and Agent-Based Simulation for Sustainable Residential Water Demand Management in the Global South

Abstract Karachi, Pakistan’s largest city, faces serious challenges in the fair and equitable distribution of water among its seven administrative divisions. To address the growing scarcity of water, fairly and equitably, this study develops an integrated Nash equilibrium and agent-based simulation for sustainable residential demand management. The approach is divided into two parts. In the first part, we present an agent-based model (ABM) developed in NetLogo, which simulates water allocation dynamics across the seven administrative divisions of the city. The model incorporates both demand-driven (e.g., water-saving behaviour, theft, and adaptive demand reduction) and supply-driven (e.g., infrastructure expansion) scenarios to evaluate system responses under varying scarcity conditions. It implements a proportional allocation strategy while simulating government interventions when water stress exceeds a certain threshold. In the second part, the Nash Bargaining Solution (NBS) is applied to address situations where supply falls short of demand in selected scenarios characterized by extreme water shortages. The scenarios, representing extreme cases of supply-demand gap, and NBS are used to reallocate the water between the seven districts fairly and efficiently. The inclusion of NBS, which is a game-theoretic approach, ensures that agents (in this case, the city divisions or districts) are allocated water based on negotiated outcomes that reflect their vulnerabilities and needs, resulting in greater fairness and equity of access to scarce water resources. We demonstrate how an agent-based model can be coupled with the cooperative bargaining solution to offer insights onto adaptive water governance, supporting equitable water distribution in heavily populated water-stressed urban cities.