A game theoretic analysis of a closed-loop water-energy nexus: The effect of technology efficiency and market competition on the market equilibrium and social welfare

Water and energy are two scarce and concerning resources interconnected in the closed-loop water-energy nexus, exemplifying the co-dependence of water and energy production. In this article, we investigate the interaction between the industries of these two resources and model it as a simultaneous game. We consider a supply chain that consists of water suppliers (WSs), power suppliers (PSs), and consumers of these commodities. In the supply chain, WSs purchase power from the power market, and PSs purchase water from the water market. Other consumers can also buy these resources at the water and power markets. The prices of these commodities depend on their quantities supplied to the markets. Each firm tries to maximize its own profit, in doing so the suppliers of water and power decide their production quantities. In this research, the Nash equilibria of the firms are determined and a comparative statics is performed on various economic measures. When there are multiple equilibria, the analysis finds the Pareto optimal equilibrium. We find that when there is sufficient supply to meet the demand of both industries and consumers, improvement of production technology improves social welfare and other economic measures of the supply chain. We also find that higher competition in either industry improves all economic measures. However, when either water or power supply is solely consumed by the firms in the cross industry, improvement of technology and higher competition can have a negative effect on some measures.