A Differential Game for Optimal Water Price Management

Andrea Caravaggio, Luigi De Cesare and Andrea Di Liddo ()
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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

Games, 2023, vol. 14, issue 2, 1-15

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.

Keywords: water management; differential games; pricing (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2023
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