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A Differential Game for Optimal Water Price Management

Author

Listed:
  • Andrea Caravaggio

    (Department of Economics, University of Foggia, 71121 Foggia, Italy)

  • Luigi De Cesare

    (Department of Economics, University of Foggia, 71121 Foggia, Italy)

  • Andrea Di Liddo

    (Department of Economics, University of Foggia, 71121 Foggia, Italy)

Abstract

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.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jgames:v:14:y:2023:i:2:p:33-:d:1116304
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    References listed on IDEAS

    as
    1. Georg Meran & Christian von Hirschhausen, 2009. "Increasing Block Tariffs in the Water Sector: A Semi-Welfarist Approach," Discussion Papers of DIW Berlin 902, DIW Berlin, German Institute for Economic Research.
    2. 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.
    3. Jeffrey A. Miron, 1996. "The Economics of Seasonal Cycles," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262133237, December.
    4. Miron, Jeffrey A & Beaulieu, J Joseph, 1996. "What Have Macroeconomists Learned about Business Cycles form the Study of Seasonal Cycles?," The Review of Economics and Statistics, MIT Press, vol. 78(1), pages 54-66, February.
    5. Phoebe Koundouri, 2004. "Current Issues in the Economics of Groundwater Resource Management," Journal of Economic Surveys, Wiley Blackwell, vol. 18(5), pages 703-740, December.
    6. Yi Xiao & Keith W. Hipel & Liping Fang, 2016. "Incorporating Water Demand Management into a Cooperative Water Allocation Framework," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(9), pages 2997-3012, July.
    7. Rubio, Santiago J. & Casino, Begona, 2001. "Competitive versus efficient extraction of a common property resource: The groundwater case," Journal of Economic Dynamics and Control, Elsevier, vol. 25(8), pages 1117-1137, August.
    8. Lambertini,Luca, 2018. "Differential Games in Industrial Economics," Cambridge Books, Cambridge University Press, number 9781107164680, November.
    9. Elkhan Richard Sadik-Zada, 2020. "Distributional Bargaining and the Speed of Structural Change in the Petroleum Exporting Labor Surplus Economies," The European Journal of Development Research, Palgrave Macmillan;European Association of Development Research and Training Institutes (EADI), vol. 32(1), pages 51-98, January.
    10. Pereau, Jean-Christophe & Pryet, Alexandre & Rambonilaza, Tina, 2019. "Optimality Versus Viability in Groundwater Management with Environmental Flows," Ecological Economics, Elsevier, vol. 161(C), pages 109-120.
    11. 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.
    12. Wenyi Du & Yubing Fan & Lina Yan, 2018. "Pricing Strategies for Competitive Water Supply Chains under Different Power Structures: An Application to the South-to-North Water Diversion Project in China," Sustainability, MDPI, vol. 10(8), pages 1-13, August.
    13. Mehdi Zomorodian & Sai Hin Lai & Mehran Homayounfar & Shaliza Ibrahim & Gareth Pender, 2017. "Development and application of coupled system dynamics and game theory: A dynamic water conflict resolution method," PLOS ONE, Public Library of Science, vol. 12(12), pages 1-24, December.
    14. Kogan, Konstantin, 2021. "Limited time commitment: Does competition for providing scarce products always improve the supplies?," European Journal of Operational Research, Elsevier, vol. 288(2), pages 408-419.
    15. Sadik-Zada, Elkhan Richard, 2023. "Resource rents, savings behavior, and scenarios of economic development," Resources Policy, Elsevier, vol. 81(C).
    16. Konstantin Kogan & Dmitry Tsadikovich & Tal Avinadav, 2022. "Water scarcity and welfare: Regulated public–private supply chain versus spot-market competition," IISE Transactions, Taylor & Francis Journals, vol. 54(8), pages 757-769, August.
    17. Konstantin Kogan & Charles Tapiero, 2010. "Water supply and consumption uncertainty: a conflict-equilibrium," Annals of Operations Research, Springer, vol. 181(1), pages 199-217, December.
    18. 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.
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