Pricing of Drinking Water under Dynamic Supply and Demand based on Government Role: A Game-Theoretic Approach

Today, managing the drinking water supply chain and its pricing have gained significant importance. This paper presents a mathematical model using game theory for the pricing of drinking water in the competitive environment comprising a Public Water System (PWS) and a Bottled Water Plant (BWP) under government intervention. This study investigates not only the role of the government in motivating BWP to increase its green manufacturing level but also analyzes supporting the PWS to enhance the quality of tap water for households. It also evaluates the government's attempts to decrease the final price of tap water by providing subsidies for households and managing tap water demand through targeted outreach programs. This paper adopts a dynamic approach to address the time-dependent nature of precipitation and water demand, incorporating uncertainty in the tap water supply. The study also introduces models for peak and volumetric water pricing, deriving several key corollaries through parametric analysis and present a case study, modeled on real-world scenarios, to validate the proposed model. This model aids in calculating the profit for each participant and provides optimal numerical results for decision variables. Finally, the research concludes with a quantitative evaluation of the impact of these findings on key parameters, providing valuable managerial insights. The results reveal that while low tap water users benefit from cost savings due to incentives, by increasing 10% of this group PWS can accrue 23.36% more benefits. Besides, reducing the PWS's demand sensitivity to price gaps by 10% can boost PWS and BWP profits by 25% and 55%, respectively.