Groundwater use under incomplete information

Abstract

This paper introduces a game theoretic model of groundwater extraction in a two-cell aquifer under incomplete information. A novel assumption is that individual users have incomplete knowledge of the speed of lateral flows in the aquifer: although a user is aware that his neighbor's water use has some influence on his future water stock, he is uncertain about the degree of this impact. We find that the lack of information may either increase or decrease the rate of water use and welfare. In a two-period framework, the relevant characteristic is the ratio of the periodic marginal benefits of water use. Depending on whether this ratio is convex or concave, the average speed with which the aquifer is depleted decreases or increases when users learn more about the local hydrologic properties of groundwater. In principle, welfare may decrease even in cases when the groundwater allocation is closer to the efficient groundwater allocation.

Groundwater pumping and spatial externalities in agriculture

“…In the case of groundwater or other resources where property rights exist, but may be incomplete because spatial movement of the resource makes it impossible to fully capture what is technically owned, the measurement of this spatial movement is important because it quantifies the resulting inefficiency. The externalities resulting from groundwater pumping from a common aquifer have been extensively discussed and their importance debated [10,15,11,27,32,35,26,5,36], but this paper is the first to measure them empirically.…”

“…While some assert that the difference between an optimal control aquifer management solution and the competitive outcome is not large enough to justify the use of costly management measures (for example, [15,14,35]), others maintain that the difference can be substantial, and that the over-extraction occurring in many of the world's aquifer basins is evidence of externality-induced over-exploitation (for example, [2,8,20,29]). Recently, economists have begun incorporating more realistic hydrological assumptions into their models, moving away from the ''bathtub'' model of an aquifer that assumes water withdrawn by one user lowers the water table instantly and uniformly throughout the entire aquifer [36,6]. These models have imparted additional insight on the problem, particularly the spatial heterogeneity of the externality, but they generally rely on parametrized mathematical programming and simulation models to predict the effect of pumping on neighboring users.…”

“…Brozovic et al [5] and Saak and Peterson [36] point out that these models ignore the most basic of hydrological rules. They employ a ''bathtub'' model of an aquifer, which assumes instantaneous lateral flow of water.…”

Groundwater Spatial Dynamics and Endogenous Well Location

“…Negri (1989), Dixon (1989), Provencher and Burt (1993), and Rubio and Casino (2003) derived competitive pumping levels as a Nash equilibrium in feedback strategies, where pumping depends on the reserve stock of water. More recently, Athanassoglou et al (2011) and Saak and Peterson (2007) build on both game-theoretic and spatial groundwater models. While considering strategic interaction by deriving feedback strategies is a more realistic hypothesis, the calculation of the equilibrium requires the solution of a very complex set of equations, 3 so we decide to derive an open-loop equilibrium (the mathematical model is detailed in Online Resource 1).…”

An agent-based platform for simulating complex human–aquifer interactions in managed groundwater systems

“…Tools such as simulation-optimisation (Barlow et al, 2003;Young, 1983, 1970;Morel Seytoux, 1975;Raul and Panda, 2013;Sedki and Ouazar, 2011;Young and Bredehoeft, 1972), evolutionary algorithms (BabbarSebens andMinsker, 2010, 2012;McKinney and Lin, 1994;Mirghani et al, 2009), econometric models (Brozovic et al, 2010;Katic and Grafton, 2012;Wan et al, 2012), game theory (Negri, 1989;Raquel et al, 2007;Saak and Peterson, 2007), and Bayesian networks (Henriksen and Barlebo, 2008;Henriksen et al, 2007;Portoghese et al, 2013) focus on equilibrium states (e.g., a global optimum, a Nash equilibrium), and describe social processes in an aggregate manner (e.g., using an optimisation function, a differential equation, a payoff matrix, etc.) based on the concept of a 'typical' agent assumed to be on average rational i.e.…”