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Rubio, Santiago J.; Casino, Begoña

doi:10.1023/a:1025637705488

Cited by 37 publications

(5 citation statements)

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“…where k r , k B > 0, A r , A B ≥ 0 and −π ≤ ϕ B ≤ π. 6 All the numerical exercises were performed, without loss of generality, by neglecting to consider the scrap value and applying the following parameter set:…”

Section: Numerical Resultsmentioning

confidence: 99%

“…In this regard, see, for example, [27,28]. 6 The function defined in (20) has period T = 1, while the function in (21) has period τ.…”

Section: Proof Ofmentioning

confidence: 99%

“…Assuming the concavity of the objective function of the problem, the model proposed by [4] shows that the feedback solution increases inefficiency with respect to a socially optimal outcome (derived from optimal control). Subsequently, in [5,6], differential games, studying open-loop and feedback scenarios over an infinite planning horizon, were proposed and used to analytically determine "social optimum" solutions. The results emerging from the analysis coordinated with those observed in [2].…”

Section: Introductionmentioning

confidence: 99%

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A Differential Game for Optimal Water Price Management

Caravaggio

Cesare

Liddo

2023

Games

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This article studies a leader–follower differential game with a finite horizon, where a single buyer reacts to the selling price set by an agency (water supplier). The Open-Loop Stackelberg equilibrium is calculated, assuming that the user demand is fully satisfied (that is, the interior solution is considered), and the following different tariff schemes are analyzed: linear scheme, increasing block tariff, and convex tariff. Numerical simulations highlight how tariff convexity and seasonality in buyer’s preferences affect water price and demand, and the dynamics of the basin over time. The study shows that synchrony or asynchrony between basin recharge and buyer cyclical demand can dramatically affect the dynamics and basin levels observed at the end of the time period considered. Additionally, the presence of a large number of fluctuations in buyer preferences affects basin fluctuations, while natural recharge may help in maintaining acceptable levels of future water demands.

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Section: Numerical Resultsmentioning

confidence: 99%

“…In this regard, see, for example, [27,28]. 6 The function defined in (20) has period T = 1, while the function in (21) has period τ.…”

Section: Proof Ofmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Differential Game for Optimal Water Price Management

Caravaggio

Cesare

Liddo

2023

Games

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“…A temporal externality (also referred to as "stock" or "strategic" externality in Provencher and Burt (1993)) arises when agents are incentivized to pump more to appropriate the resource first. This type of externality emerges from the finite nature of groundwater resources and are most salient when the aquifer is near depletion (Rubio & Casino, 2003). A spatial externality also emerges because pumping by individual users affects groundwater levels faced by the other users of the aquifer, and hence their pumping costs (Brozović et al, 2010).…”

mentioning

confidence: 99%

Hydro Economic Asymmetries and Common‐Pool Overdraft in Transboundary Aquifers

Mullen

Müller

Penny

et al. 2022

Water Resources Research

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The common‐pool nature of groundwater resources creates incentives to over pump that contribute to their rapid global depletion. In transboundary aquifers, users are separated by a territorial border and might face substantially different economic and hydrogeologic conditions that can alternatively dampen or amplify incentives to over pump. We develop a theoretical model that couples principles of game theory and groundwater flow to capture the combined effect of well locations and user asymmetries on pumping incentives. We find that heterogeneities across users (here referred to as asymmetries) in terms of either energy cost, groundwater profitability or aquifer response tend to dampen incentives to over pump. However, combinations of two or more types of asymmetry can substantially amplify common‐pool overdraft, particularly when the same user simultaneously faces comparatively higher costs (or aquifer response) and profitability. We use this theoretical insight to interpret the emergence of the Disi agreement between Saudi Arabia and Jordan in association with the Disi‐Amman water pipeline. By using bounded non‐dimensional parameters to encode user asymmetries and groundwater connectivity, the theory provides a tractable generalized framework to understand the premature depletion of shared aquifers, whether transboundary or not.

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“…There is a large body of literature dealing with applications of modeling, optimal control, and game theory methods to the groundwater depletion problem (for example, Bredehoeft & Young, 1970;Brozovic et al, 2010;Burt, 1966Burt, , 1967Gisser & Sanchez, 1980;Madani & Dinar, 2012a, 2012bMüller et al, 2017;Negri, 1989;Provencher & Burt, 1993;Rubio & Casino, 2001, 2003Sahu, 2018a). Much of this literature poses groundwater depletion as a type of common pool problem (Gardner et al, 1990;Hardin, 1968;Madani & Dinar, 2012a;Ostrom, 1990).…”

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confidence: 99%

The Multi‐Scale Dynamics of Groundwater Depletion

Sahu

McLaughlin

2021

Water Resources Research

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The depletion of groundwater resources is a widespread phenomenon that can jeopardize both water and food security by making groundwater less accessible, degrading water quality, reducing surface water flow, and compromising the buffering capacity provided by groundwater reserves (Aeschbach-Hertig & Gleeson, 2012). There is abundant documentation of the severity and extent of groundwater depletion, especially in intensively cultivated areas (Bierkens & Wada, 2019;Gleeson et al., 2012). However, undesirable depletion occurs despite knowledge of the problem among water users and despite evidence that effective management and cooperation can reduce the adverse effects of exploitation (Madani & Dinar, 2012b;Ostrom, 1990).Here we address some basic questions about the physical and economic aspects of long-term groundwater depletion. What controls pumping decisions in an unconfined aquifer with multiple wells operated by different users? Can cooperation among the aquifer users increase the benefits and reduce the adverse impacts of pumping? What are the revenue and environmental implications of well yield limitations and regulatory constraints? How are the effects of pumping distributed between storage depletion and reductions in aquifer outflow? These research questions address groundwater depletion issues that are long-standing but have largely remained unresolved, at least in any quantitative sense. Quantitative answers to these questions can provide useful insight about how depletion occurs and how it might be reduced.In order to address our research questions, we need to consider the economically driven pumping decisions made by the agents who use the aquifer (e.g., farmers or irrigation districts) as well as physical processes and policies that may constrain these decisions. One way to include decision-making is to treat pumping rates as time-dependent variables (rather than inputs) that agents continually adjust to maximize particular objectives. This perspective naturally leads to an optimal control formulation of the decision problem. Solutions to this problem describe the pumping and storage histories that can be expected for particular aquifers and management strategies. The optimization process is constrained by physical groundwater flow constraints and by well yield and regulatory constraints that may limit pumping.The constraints required in this decision-driven approach to depletion analysis need to consider local conditions at the well scale, which guide pumping decisions, as well as conditions at larger aquifer scales where the economic and environmental impacts of agent decisions are felt. Consequently, the relevant spatial scales for our

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Cited by 37 publications

References 0 publications

A Differential Game for Optimal Water Price Management

A Differential Game for Optimal Water Price Management

Hydro Economic Asymmetries and Common‐Pool Overdraft in Transboundary Aquifers

The Multi‐Scale Dynamics of Groundwater Depletion

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