A water distribution problem in the Mexican Valley is modeled first as a three-person noncooperative game. Each player has a five-dimensional strategy vector, the strategy sets are defined by 15 linear constraints, and the three payoff functions are also linear. A nonlinear optimization problem is first formulated to obtain the Nash equilibrium based on the Kuhn-Tucker conditions, and then, duality theorem is used to develop a computational procedure. The problem can also be considered as a conflict between the three players. The non-symmetric Nash bargaining solution is suggested to find the solution. Multiobjective programming is an alternative solution concept, when the water supply of the three players are the objectives, and the water authority is considered to be the decision maker. The optimal water distribution strategies are determined by using these solution concepts and methods.
Cite this paper
A. Ahmadi and R. Moreno, "Game Theory Applications in a Water Distribution Problem," Journal of Water Resource and Protection
, Vol. 5 No. 1, 2013, pp. 91-96. doi: 10.4236/jwarp.2013.51011
 F. Forgo, J. Szep and F. Szidarovszky, “Introduction to the Theory of Games,” Kluwer Academic Publishers, Dordrecht, 1999.
 L. R. Brown, “Outgrowing the Earth: The Food Security Challenge in an Age of Falling Water Tables and Rising Temperatures,” Earthscan Publications Ltd., London, 2005.
 J. C. Harsanyi and R. Selten, “A Generalized Nash Solution for Two-Person Bargaining Games with Incomplete Information,” Management Science, Vol. 18, No. 5, 1972, pp. 80-106. doi:10.1287/mnsc.18.5.80
 E. A. Roth, “Axiomatic Methods of Bargaining,” Springer-Verlag, Berlin, 1979. doi:10.1007/978-3-642-51570-5
 F. Szidarovszky, M. Gershon and L. Duckstein, “Techniques of Multiobjective Decision Making in Systems Management,” Elsevier, Amsterdam, 1986.
 K. W. Hipel, “Multiple Objective Decision Making in Water Resources,” Water Resources Bulletin, Vol. 28, No. 1, 1992, pp. 3-11. doi:10.1111/j.1752-1688.1992.tb03150.x
 J. J. Bogardi and H. P. Nachtnebel, “Multi-Criteria Decision Analysis in Water Resources Management,” UNE-SCO Publication SC94/WS.14, UNESCO, Paris, 1994.
 K. Donevska, S. Dodeva and J. Tadeva, “Urban and Agricultural Competition for Water in the Republic of Macedonia,” 2003.
 P. K. Jensen, W. V. D. Hoek, F. Konradsen and W. A. Jehangir, “Domestic Use of Irrigation Water in Punjab,” 24th WEDC Conference Sanitation and Water for All Islamabad, Islamabad, 1998.
 Z. S. Kapelan, D. A. Savic and G. A. Walters, “Multi-objective Design of Water Distribution Systems under Uncertainty,” Water Resources Research, Vol. 41, No. 11, 2005. doi:10.1029/2004WR003787
 E. G. Bekele and J. W. Nicklow, “Multiobjective Management of Ecosystem Services by Integrative Watershed Modeling and Evolutionary Algorithms,” Water Resources Research, Vol. 41, 2005.
 L. Z. Wang, L. P. Fang and K. W. Hipel, “Basin Wide Cooperative Water Resources Allocation,” European Journal of Operational Research, Vol. 190, No. 3, 2008, pp. 798-817. doi:10.1016/j.ejor.2007.06.045
 R. Salazar, F. Szidarovszky and A. Rojano, “Water Distribution Scenarios in the Mexican Valley,” Water Resources Management, Vol. 24, No. 12, 2010, pp. 2959-2970. doi:10.1007/s11269-010-9589-9