Optimal Groundwater Policy in the Presence of Farmers’ Productivity Investment: A Dynamic Game Approach (in Persian)

In many arid and semi-arid regions, shared groundwater aquifers play a crucial role in sustaining agricultural production, while the absence of effective institutions has exacerbated over-extraction and groundwater depletion. This paper develops a theoretical framework to analyze the interaction between local policy-making, investment in efficiency, and informal water trading. The model is formulated as a dynamic, sequential game with complete information among three players: a local planner, a high-productivity farmer, and a low-productivity farmer. The local planner determines groundwater extraction quotas to maximize discounted social welfare; the low-productivity farmer sells part of his quota in an informal market; and the high-productivity farmer dynamically decides on the level of investment in productivity-enhancing technologies. The dynamics of capital accumulation and groundwater levels are modeled through differential equations, and the game equilibrium is derived using Pontryagin’s Maximum Principle and backward induction. The results indicate that investment in productivity not only increases private profits but also contributes to aquifer sustainability by reducing water demand. Moreover, institutional and environmental parameters—such as the discount rate, aquifer recharge (or permeability) coefficient, and the valuation of environmental externalities—play a decisive role in determining optimal water allocation policies. The findings underscore the necessity of coordinating water allocation policies with investment incentives for water-efficient technologies.