Water Costs Allocation in Complex Systems Using a Cooperative Game Theory Approach

The management of complex water resource systems that address water service recovery costs and consider adequate contributions and priorities require methods that integrate technical, economic, environmental, social and legal aspects into a comprehensive framework. In Europe, the Water Framework Directive (WFD) 2000/60/EC recommends that the pricing politics in a river basin take into account the cost recovery and the economic sustainability of the water use. However, the current cost allocation methods do not consider the user’s willingness to pay and often do not permit a total cost recovery. Thus, a new approach is required that includes these requirements when defining water rates. This article presents a methodology to allocate water service costs in a water resource system among different users that attempts to fulfil the WFD requirements. The methodology is based on Cooperative Game Theory (CGT) techniques and on the definition of the related characteristic function using a mathematical optimisation approach. The CGT provides the instruments that are necessary to analyse situations that require a cost-sharing rule. The CGT approach can define efficient and fair solutions that provide the appropriate incentives among the parties involved. Therefore, the water system cost allocation has been valued as a game in which it is necessary to determine the right payoff for each player that is, in this case, a water user. To apply the CGT principles in a water resources system, the characteristic function needs to be defined and evaluated using an adequate modelling approach; in this study, it is evaluated using the optimisation model WARGI. (Sechi and Zuddas 2000). The so-called “core” represents the game-solution set. It represents the area of the admissible cost allocation values from which the boundaries on the cost values for each player can be supplied. Within the core lie all of the allocations that satisfy the principles of equity, fairness, justice, efficiency and that guarantee cost recovery. The core of a cooperative game can represent a useful instrument to define the water cost rates. Furthermore, it can be used as a valid support in water resource management to achieve the economic analysis required by the WFD. The methodology was applied to a multi-reservoir and multi-demand water system in Sardinia, Italy.