Dynamic Stackelberg game model for water rationalization in drought emergency

In water resource management, in case of a limited resource, there is a conflict situation between different consumers. In this paper, a dynamic game-theoretical model is suggested for the solution of such conflict. Let us suppose that in a region, water supply is based on a given aquifer, from which a quantity of effective reserve can be used without damaging the aquifer, and a long drought is foreseen. The use of water is divided between the social sector represented by the local authority, and the production sector, in our case, simplified to a single agricultural producer using water for irrigation; they are the players in the game. For a fixed time period, every day, a given amount is available, from which first the authority, then the producer takes a proportion, which corresponds to the strategy choices of the players. A price function is given, which depends on the total available reserve, the payoffs of both players are quantified as their net incomes for the whole period: for the producer: profit from selling the product minus price of water and tax paid, for the authority: tax received plus the gain for the authority from selling the water bought to the social sector minus price of water purchased. A solution (equilibrium) of the game consists of such strategy choices of both players, with which each player maximizes her/his total payoff (over the whole time horizon of the game) provided that the other player also maximizes her/his own payoff. In the paper, in a mathematical model for the above conflict situation, a deterministic continuum-strategy two-player discrete-time dynamic Stackelberg game with fixed finite time duration and closed-loop information structure is proposed, where the authority is "leader" and the producer is "follower". The algorithms for the solution of the game are based on recent theoretical results of the authors. Illustrative numerical examples are also given. (C) 2014 Elsevier B.V. All rights reserved.