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A Novel Solution for Stochastic Dynamic Game of Water Allocation from a Reservoir Using Collocation Method

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  • Mehran Homayounfar
  • Arman Ganji
  • C. Martinez

Abstract

In this study, a continuous model of stochastic dynamic game for water allocation from a reservoir system was developed. The continuous random variable of inflow in the state transition function was replaced with a discrete approximant rather than using the mean of the random variable as is done in a continuous model of deterministic dynamic game. As a result, a new solution method was used to solve the stochastic model of game based on collocation method. The collocation method was introduced as an alternative to linear-quadratic (LQ) approximation methods to resolve a dynamic model of game. The collocation method is not limited to the first and second degree approximations, compared to LQ approximation, i.e. Ricatti equations. Furthermore, in spite of LQ related problems, consideration of the stochastic nature of game on the action variables in the collocation method would be possible. The proposed solution method was applied to the real case of reservoir operation, which typically requires considering the effect of uncertainty on decision variables. The results of the solution of the stochastic model of game are compared with the results of a deterministic solution of game, a classical stochastic dynamic programming model (e.g. Bayesian Stochastic Dynamic Programming model, BSDP), and a discrete stochastic dynamic game model (PSDNG). By comparing the results of alternative methods, it is shown that the proposed solution method of stochastic dynamic game is quite capable of providing appropriate reservoir operating policies. Copyright Springer Science+Business Media B.V. 2011

Suggested Citation

  • Mehran Homayounfar & Arman Ganji & C. Martinez, 2011. "A Novel Solution for Stochastic Dynamic Game of Water Allocation from a Reservoir Using Collocation Method," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 25(13), pages 3427-3444, October.
    • Handle: RePEc:spr:waterr:v:25:y:2011:i:13:p:3427-3444
    DOI: 10.1007/s11269-011-9863-5
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    References listed on IDEAS

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    Cited by:

    1. Maryam Ghashghaie & Safar Marofi & Hossein Marofi, 2014. "Using System Dynamics Method to Determine the Effect of Water Demand Priorities on Downstream Flow," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(14), pages 5055-5072, November.
    2. Sabah Fayaed & Ahmed El-Shafie & Othman Jaafar, 2013. "Integrated Artificial Neural Network (ANN) and Stochastic Dynamic Programming (SDP) Model for Optimal Release Policy," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(10), pages 3679-3696, August.
    3. Mehdi Zomorodian & Sai Hin Lai & Mehran Homayounfar & Shaliza Ibrahim & Gareth Pender, 2017. "Development and application of coupled system dynamics and game theory: A dynamic water conflict resolution method," PLOS ONE, Public Library of Science, vol. 12(12), pages 1-24, December.
    4. Mehran Homayounfar & Sai Lai & Mehdi Zommorodian & Amin Oroji & Arman Ganji & Sara Kaviani, 2015. "Developing a Non-Discrete Dynamic Game Model and Corresponding Monthly Collocation Solution Considering Variability in Reservoir Inflow," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(8), pages 2599-2618, June.
    5. Mohammad Ehteram & Samira Ghotbi & Ozgur Kisi & Ahmed EL-Shafie, 2019. "Application of a Coordination Model for a Large Number of Stakeholders with a New Game Theory Model," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(15), pages 5207-5230, December.
    6. Xiqin Wang & Yuan Zhang & Yong Zeng & Changming Liu, 2013. "Resolving Trans-jurisdictional Water Conflicts by the Nash Bargaining Method: A Case Study in Zhangweinan Canal Basin in North China," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(5), pages 1235-1247, March.

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