Differential Game Theoretic Models for Designing Water Conservation Incentives

Abstract

The growing concern over water scarcity and the management of freshwater is common worldwide. Voluntary incentives, such as payments offered to water users, are recognized as a strategy for reducing conflicts and water consumption. A primary challenge lies in determining the allocation of these incentives among water users, taking into account socio-environmental factors. This study leverages differential game theoretic models to design incentive schemes for the network of water users, geographically distributed across a river network. Two networks of water users are considered: those who utilize groundwater and those who rely on surface water for agricultural purposes. A nongovernmental organization (NGO) participates as another key player, providing conservation incentives to encourage water users to reduce their consumption. The proposed model considers both vertical and horizontal interactions within the network of players. By considering the unique characteristics of each water user, the NGO aims to introduce an incentive scheme designed for each water user. Addressing the challenge of model scalability becomes crucial as the number of players or water users within each network increases, in order to identify optimal decisions. Thus, we propose solution methods for both convex and nonconvex decision problems using Karush-Kuhn-Tucker conditions, Value Iteration, and Basis Function Approximation methods. Finally, we perform parametric analyses to examine how parameters influence the choice of solution methods and affect the decision-making processes. Funding: Financial support from the U.S. National Science Foundation [Grant 2108003] is gratefully acknowledged.