Time-Consistent Fair Water Sharing Agreements

  • Rodney Beard
  • Stuart McDonald
Part of the Annals of the International Society of Dynamic Games book series (AISDG, volume 9)


Scarcity of water has become a major issue facing many nations around the world. To improve the efficiency of water usage there has been considerable interest in recent years in trading water. A major issue in trading water rights is the problem of how an allocation system can be designed in perpetuity that also has desirable properties at each point of time. This is an issue of the time consistency of the contract to trade water. In this chapter we develop a model of dynamic recontracting of water rights and study time consistency properties of the resultant contracts using the ideas of Filar and Petrosjan [7].

Key words

Dynamic cooperative games water sharing agreements time consistency of contracts 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Ambec, S. and Y. Sprumont(2002) Sharing a River, Journal of Economic Theory, Vol. 107, pp. 453–462.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    Burness, H.S. and J.P. Quirk (1979) Appropriative Water Rights and the Efficient Allocation of Resources, The American Economic Review, Vol. 69, pp. 25–37.Google Scholar
  3. [3]
    Burness, H.S. and J.P. Quirk (1980) Economic aspects of appropriative water rights, Journal of Environmental Economics and Management, Vol. 7, pp. 372–388.CrossRefGoogle Scholar
  4. [4]
    Casas-Mendez, B., I. Garcia-Jurado, A. van den Nouweland and M. Vazquez-Brage (2003) An extension of the ?-value to games with coalition structures, European Journal of Operational Research, Vol. 148, pp. 494–513.zbMATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    Curiel, I., Pederzoli, G. and S. Tijs (1989) Sequencing Games, European Journal of Operational Research, Vol. 40, pp. 344–351.zbMATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    Dementieva, M. (2004) Regularization in Multistage Cooperative Games, PhD Thesis, Jvaskala Studies in Computing no. 42, University of Jyvaskala.Google Scholar
  7. [7]
    Filar, J.A. and L.A. Petrosjan (2000) Dynamic Cooperative Games, International Game Theory Review Vol. 2, no. 1, pp. 47–65.zbMATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    Firoozi, F. and J. Merrifield (2003) An Optimal Timing Model of Water Reallocation and Reservoir Construction, European Journal of Operational Research, Vol. 145, pp. 165–174.zbMATHCrossRefGoogle Scholar
  9. [9]
    Freebairn, J. and J. Quiggin (2004) Water Rights for Variable Supplies, Risk and Sustainable Management Group, Murray Darling Program Working Paper:2/M04, School of Economics, The University of Queensland.Google Scholar
  10. [10]
    Greenberg, J. and S. Weber (1986) Strong Tiebout Equilibrium under Restricted Preferences Domain, Journal of Economic Theory, Vol. 38, pp. 101–117.zbMATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    Hendrickx, R. (2004) Cooperation and Allocation, PhD Thesis, CenTeR, University of Tilburg.Google Scholar
  12. [12]
    Howe, C.W., D.R. Schurmeier and W. Douglas Shaw, Jr. (1986) Innovative approaches to water allocation: the potential for water markets, Water Resources Research, Vol. 22, no. 4, pp. 439–445.CrossRefGoogle Scholar
  13. [13]
    Lahmandi-Ayed, R. and M-S. Matoussi (2002) Long-Term Effects of Water Markets: Investing or Rent-seeking? CERMSEM Universite de Paris I Serie Bleu 2002.11, CERMSEM Universite de Paris I.Google Scholar
  14. [14]
    Meinzen-Dick, R.S. and R. Pradhan (2002) Legal Pluralism and Dynamic Property Rights CAPRi Working paper No. 22 CGIAR System Wide Program on Collective Action and Property Rights, International FoodPolicy Research Institute.Google Scholar
  15. [15]
    Myerson, R.B. (1977) Graphs and Cooperation in Games, Mathematics of Operations Research, Vol. 2 no. 3 pp. 225–230.zbMATHMathSciNetCrossRefGoogle Scholar
  16. [16]
    Petrosjan, L.A. (2005) Cooperative Differential Games, in: A. Nowak, K. Szajowski (Eds.) Advances in Dynamic Games: Applications to Economics, Fianance, Optimization and Stochastic Control, Annals of Dynamic Games 7, Birkhäuser.Google Scholar
  17. [17]
    Petrosjan, L.A. and G. Zaccour (2003) Time Consistent Shapley Value Allocation of Pollution Cost Reduction, Journal of Economic Dynamics and Control., Vol. 27, pp. 381–398.zbMATHCrossRefMathSciNetGoogle Scholar
  18. [18]
    Petrosjan, L.A. and N.A. Zenkevich (1996) Game Theory, World Scientific, Singapore.Google Scholar
  19. [19]
    Provencher, B. (1993) A Private Property Rights Regime to Replenish a Groundwater Aquifer, Land Economics, Vol. 69, pp. 325–40.CrossRefGoogle Scholar
  20. [20]
    Provencher, B. and O. Burt(1994) A Private Property Rights Regime for the Commons: the case for Groundwater, American Journal of Agricultural Economics, Vol. 76, pp. 875–888.CrossRefGoogle Scholar
  21. [21]
    Tarashnina, S. (2002) Time-Consistent Solution of a Cooperative Group Pur-suit Game, International Game Theory Review, Vol. 4, no. 3, pp. 301–317.zbMATHCrossRefMathSciNetGoogle Scholar
  22. [22]
    Zakharov, V. and M. Dementieva (2004) Multistage Cooperative Games and the Problem of Time Consistency, International Game Theory Review, Vol. 6, no. 1, pp. 156–170.CrossRefMathSciNetGoogle Scholar

Copyright information

© Birkhäuser Boston 2007

Authors and Affiliations

  • Rodney Beard
    • 1
  • Stuart McDonald
    • 1
  1. 1.School of Economics and the ARC Centre for Complex SystemsThe University of QueenslandQueenslandAustralia

Personalised recommendations