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Groundwater extraction among overlapping generations: a differential game approach

Author

Listed:
  • Marta Biancardi

    (University of Bari)

  • Lucia Maddalena

    (University of Foggia)

  • Giovanni Villani

    (University of Bari)

Abstract

Groundwater is a common resource that has been wasted for years. Today, we pay the consequences of such inappropriate exploitation and we are aware that it is necessary to realize policies in order to guarantee the use of this resource for future generations. In fact, the irrational exploitation of water by agents, nevertheless it is a renewable resource, may cause its exhaustion. In our paper, we develop a differential game to determine the efficient extraction of groundwater resource among overlapping generations. We consider intragenerational as well as intergenerational competition between extractors that exploit the resource in different time intervals, and so the horizons of the players in the game are asynchronous. Feedback equilibria have been computed in order to determine the optimal extraction rate of “young” and “old” agents that coexist in the economy. The effects of the withdrawal by several generations are numerically and graphically analyzed in order to obtain results on the efficiency of the groundwater resource.

Suggested Citation

  • Marta Biancardi & Lucia Maddalena & Giovanni Villani, 2020. "Groundwater extraction among overlapping generations: a differential game approach," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 539-556, December.
    • Handle: RePEc:spr:decfin:v:43:y:2020:i:2:d:10.1007_s10203-020-00292-w
    DOI: 10.1007/s10203-020-00292-w
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    References listed on IDEAS

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    1. Santiago Rubio & Begoña Casino, 2003. "Strategic Behavior and Efficiency in the Common Property Extraction of Groundwater," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 26(1), pages 73-87, September.
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    8. Esteban, Encarna & Albiac, José, 2011. "Groundwater and ecosystems damages: Questioning the Gisser-Sánchez effect," Ecological Economics, Elsevier, vol. 70(11), pages 2062-2069, September.
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    Cited by:

    1. Andrea Caravaggio & Luigi De Cesare & Andrea Di Liddo, 2023. "A Differential Game for Optimal Water Price Management," Games, MDPI, vol. 14(2), pages 1-15, April.
    2. Marta Biancardi & Gianluca Iannucci & Giovanni Villani, 2022. "Groundwater Exploitation and Illegal Behaviors in a Differential Game," Dynamic Games and Applications, Springer, vol. 12(3), pages 996-1009, September.
    3. Marta Biancardi & Gianluca Iannucci & Giovanni Villani, 2023. "Groundwater management and illegality in a differential-evolutionary framework," Computational Management Science, Springer, vol. 20(1), pages 1-17, December.

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    More about this item

    Keywords

    Differential games; Resource extraction; Overlapping generation; Feedback Nash equilibrium;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • Q25 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Water
    • J11 - Labor and Demographic Economics - - Demographic Economics - - - Demographic Trends, Macroeconomic Effects, and Forecasts
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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