Advertisement

Water Resources Management

, Volume 27, Issue 6, pp 1781–1796 | Cite as

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

  • Giovanni M. Sechi
  • Riccardo Zucca
  • Paola Zuddas
Article

Abstract

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.

Keywords

Water resource system management Cost allocation Water pricing 

References

  1. Deidda D, Andreu J, Perez MA, Sechi GM, Zucca R, Zuddas P (2009) A cooperative game theory approach to water pricing in a complex water resource system. 18th World IMACS/MODSIM Congress, Cairns, AustraliaGoogle Scholar
  2. EU (2000) Directive 2000/60/EC of the European Parliament and of the Council of 23 October 2000 establishing a framework for Community action in the field of water policy, Official Journal of the European Communities 22/12/2000Google Scholar
  3. Fragnelli V (2010) Teoria dei Giochi. Dispense di Teoria dei Giochi. Università di AlessandriaGoogle Scholar
  4. Gillies DB (1953) Some theorems on n-person games, PhD Thesis. Department of Mathematics, Princeton UniversityGoogle Scholar
  5. Griffin R (2006) Water resource economics. The analysis of scarcity, policies, and projects. The MIT Press, CambridgeGoogle Scholar
  6. ILOG (2007) CPLEX 11.0, user’s manualGoogle Scholar
  7. Lemaire J (1984) An application of game theory: cost allocation. Universitè Libre de Bruxelles. Astin Bull 14(1):61–81Google Scholar
  8. Lippai I, Heaney JP (2000) Efficient and equitable impact fees for urban water systems. J Water Resour Manag Plan 126(2):75–84CrossRefGoogle Scholar
  9. Manca A, Sechi GM, Sulis A, Zuddas P (2004) Complex water resources system optimization aided by graphical interface. VI International Conference of Hydroinformatics, SingaporeGoogle Scholar
  10. Parrachino I, Zara S, Patrone F (2002) Cooperative game theory and its application to natural, environmental and water resources issues: 1. Basic Theory. World Bank Policy Research Working Paper 4072Google Scholar
  11. Ransmeier JS (1942) The Tennessee Valley authority: a case of study in the economics of multiple purpose stream planning. Vanderbilt University Press, NashvilleGoogle Scholar
  12. RAS (2006) Piano Stralcio di Bacino Regionale per l’Utilizzo delle Risorse Idriche. Regione Autonoma della Sardegna, ItalyGoogle Scholar
  13. RAS (2008) Studio del Modello di Gestione del Sistema Idrico Regionale. Documenti Finali della Seconda Attività. Regione Autonoma della Sardegna ItalyGoogle Scholar
  14. Salis F, Sechi GM, Zuddas P (2006) Optimization model for the conjunctive use of conventional and marginal waters. In Andreu J, Rossi G, Vagliasindi F, Vela A. Drought management and planning for water resources. Taylor & FrancisGoogle Scholar
  15. Schmeidler D (1969) The nucleolus of a characteristic function game. SIAM J Appl MathGoogle Scholar
  16. Sechi GM, Sulis A (2009) Water system management through a mixed optimization-simulation approach. J Water Resour Plan Manag 135(3):160–170CrossRefGoogle Scholar
  17. Sechi GM, Zuddas P (2000) WARGI: Water Resources System Optimization Aided by graphical interface. In Blain WR, Brebbia CA. Hydraulic engineering software. WIT-Press, 2000, pp 109–120Google Scholar
  18. Shapley LS (1953) A value for n-person games. In Kuhn HW, Tucker AW. Contributions to the theory of games, vol II. Annals of Mathematics Studies No. 28. Princeton University PressGoogle Scholar
  19. Thomas AL (1974) The allocation problem, part two, studies in accounting research No. 9, American Accounting AssociationGoogle Scholar
  20. TVA (1938) Tennessee Valley authority. Allocation of investment in Norris, Wheeler and Wilson Project. US House of Representatives, Document No 709, Congress Third Session, Washington DC. US Government Printing OfficeGoogle Scholar
  21. Von Neumann J, Morgenstern O (1944) Theory of games and economic behavior. Princeton University Press, PrincetonGoogle Scholar
  22. Young HP (1985) Cost allocation: methods, principles, applications. Elsevier Science PublishersGoogle Scholar
  23. Young HP (1994) Cost allocation. In Aumann RJ, Hart S. Handbook of game theory. Elsevier Science B.V. 2(34), 1194–1234Google Scholar
  24. Young HP, Okada N, Hashimoto T (1982) Cost allocation in water resources development. Water Resour Res 18:463–475CrossRefGoogle Scholar
  25. Zucca R (2011) A Cooperative Game Theory approach for cost allocation in complex water resource systems. PhD thesis, University of Cagliari, Cagliari, http://veprints.unica.it/551/1/PhD_Riccardo_Zucca.pdf

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Giovanni M. Sechi
    • 1
  • Riccardo Zucca
    • 1
  • Paola Zuddas
    • 1
  1. 1.Department of Land EngineeringUniversity of CagliariCagliariItaly

Personalised recommendations