Competition between different groundwater uses under water scarcity

Cachorro, Julia de Frutos; Marín-Solano, Jesús; Navas, Jorge

doi:10.1016/j.wre.2020.100173

Cited by 6 publications

(13 citation statements)

References 27 publications

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“…First, in this study agents are supposed to have different water demand as opposed to the classical studies of Gisser and Sanchez (1980) [12], Rubio and Casino (2001) [22], and Esteban and Albiac (2011) [8], where agents were considered to be identical in their demand for the water resource. Also unlike Roseta-Palma and Brasão [21] and de Frutos Cachorro et al (2020) [11], who have already considered the asymmetry in water demand for different uses (farming and public supply), the agents in this study are using the groundwater for the same purpose -irrigation of crops -and have the same elasticity of demand (both agents are farmers and they differ in the land size -hence the difference in the amount of water in demand, but not in demand elasticity). Second, as the size of land of two farmers (a small farmer and a big farmer) is not the same there is no reason to assume that the future discount rates will be the same, as well stated in de-Paz et al [18].…”

Section: Introductionmentioning

confidence: 91%

“…It means that the solution computed at time t is no longer optimal for t > t, and modified dynamic programming equations are required. The study of de Frutos Cachorro et al (2020) [11], the most similar to this work, analysed both demand and discount rate asymmetries in the context of groundwater use for different purposes, comparing cooperation versus non-cooperation equilibria. The results of this study showed that cooperation is more efficient in terms of stock than non-cooperative solutions, but that in terms of personal welfare the cooperation is not always profitable.…”

Section: Introductionmentioning

confidence: 97%

“…So, here we also depart from classical studies in assuming different discount rates of agents. Moreover, in contrast to de Frutos Cachorro et al (2020) [11], who considered different discount rates of agents before the occurrence of a regime shift in the aquifer (change of the natural recharge rate), in this paper different discount rates are applied to the infinite planning horizon.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Groundwater Extraction for Irrigation Purposes: The Case of Asymmetric Players

Chukaeva,

Frutos Cachorro,

Marín-Solano

2024

Water Econs. Policy

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In this paper, we address the problem of groundwater exploitation by heterogeneous farmers for irrigation purposes. In particular, we study the possible inefficiencies that can arise in this type of common resource problem by considering the dynamic and strategic interactions between groundwater users. To this end, we build a two-player differential game in which two types of farmers (or many farmers grouped into two types, with a representative farmer for each group) display different characteristics related to their agricultural activity. More precisely, they can have different water demand functions, extraction costs, crop productivity, land types and time-preferences. Conditions are studied for the existence and uniqueness of the cooperative and non-cooperative solutions asymptotically converging to a steady state. The model is then applied to the case study of the Western La Mancha aquifer. Effects of the different heterogeneities on the degree of inefficiency of non-cooperative solutions with respect to cooperative solutions are analyzed. Numerical results show that cooperation is always beneficial for the environment and for the agents: It results in higher levels of groundwater stock and total welfare. Moreover, considering heterogeneous time preferences is crucial for reducing the inefficiency of non-cooperation with respect to cooperation, regardless of the other asymmetries between farmers.

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Section: Introductionmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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Groundwater Extraction for Irrigation Purposes: The Case of Asymmetric Players

Chukaeva,

Frutos Cachorro,

Marín-Solano

2024

Water Econs. Policy

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“…Thus the problem was reduced to the problem with different discounting factors λ j (t) on the different time intervals [T j , T j+1 ) (cf. [6]).…”

Section: T L(t)mentioning

confidence: 99%

“…Later, in [2], the notion of the IDP was extended to the class of differential games with infinite duration and a discounting function of a rather general form. Since then, there have been a number of papers devoted to the analysis of optimal problems with different types of discounting functions and their extension to the class of differential games (see, e.g., [3][4][5], where this problem was considered in both deterministic and stochastic settings, and [6] for the very recent results. )…”

Section: Introductionmentioning

confidence: 99%

Time-Consistency of an Imputation in a Cooperative Hybrid Differential Game

Gromova

Malakhova

2021

Mathematics

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This work is aimed at studying the problem of maintaining the sustainability of a cooperative solution in an n-person hybrid differential game. Specifically, we consider a differential game whose payoff function is discounted with a discounting function that changes its structure with time. We solve the problem of time-inconsistency of the cooperative solution using a so-called imputation distribution procedure, which was adjusted for this general class of differential games. The obtained results are illustrated with a specific example of a differential game with random duration and a hybrid cumulative distribution function (CDF). We completely solved the presented example to demonstrate the application of the developed scheme in detail. All results were obtained in analytical form and illustrated by numerical simulations.

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Optimal water tariffs for domestic, agricultural and industrial use

Caravaggio,

De Cesare,

Di Liddo

2024

Ann Oper Res

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Consider a water supplier who determines sales rates with the goals of maximizing profits, protecting consumer welfare, and ensuring adequate future water supplies. Buyers are differentiated and can use the water for domestic, agricultural, and industrial purposes. We propose a leader-follower finite-horizon differential game. The leader (the water supplier) determines the selling price and the followers (consumers) react by requesting their optimal amount of water. We calculate a feedback Stackelberg equilibrium assuming that all user demand is satisfied (interior equilibrium). We compare two different tariff schemes: linear tariffs (the price paid is a multiple of the volume of water purchased), and increasing block tariffs (the unit price is lower for quantities of water that do not exceed a fixed threshold). We show that block pricing is never optimal and linear pricing is always preferred.

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Competition between different groundwater uses under water scarcity

Cited by 6 publications

References 27 publications

Groundwater Extraction for Irrigation Purposes: The Case of Asymmetric Players

Groundwater Extraction for Irrigation Purposes: The Case of Asymmetric Players

Time-Consistency of an Imputation in a Cooperative Hybrid Differential Game

Optimal water tariffs for domestic, agricultural and industrial use

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