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The Stackelberg games of water extraction with myopic agents

Author

Listed:
  • Alain Jean-Marie

    (NEO - Network Engineering and Operations - CRISAM - Inria Sophia Antipolis - Méditerranée - Inria - Institut National de Recherche en Informatique et en Automatique)

  • Mabel Tidball

    (CEE-M - Centre d'Economie de l'Environnement - Montpellier - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - Institut Agro - Montpellier SupAgro - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement)

  • Víctor Bucarey

    (UOH - Universidad de O'Higgins)

Abstract

We consider a discrete time, infinite horizon dynamic game of groundwater extraction.A Water Agency charges an extraction cost to water users, and controls the marginal extraction cost so that it depends, not only on the level of groundwater, but also ontotal water extraction (through a parameter n that represents the degree of strategic interactions between water users) and on rainfall (through parameter m). The water users are selfish and myopic, and the goal of the agency is to give them incentives so as to improve their total discounted welfare. We look at this problem in several situations. In the first situation, the parameters n and m are considered to be fixed over time. A first result shows that when the Water Agency is patient (the discount factor tends to 1) the optimal marginal extraction cost asks for strategic interactions between agents. The contrary holds for a discount factor near 0. In a second situation, we look at the dynamic Stackelberg game where the Agency decides at each time what cost parameter they must announce. We study theoretically and numerically the solution of this problem. Simulations illustrate the possibility thatthreshold policies are good candidates for optimal policies.

Suggested Citation

  • Alain Jean-Marie & Mabel Tidball & Víctor Bucarey, 2021. "The Stackelberg games of water extraction with myopic agents," Post-Print hal-03429257, HAL.
    • Handle: RePEc:hal:journl:hal-03429257
    DOI: 10.1142/S0219198921500237
    as

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