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

Homayounfar, Mehran; Ganji, Arman; Martinez, Christopher J.

doi:10.1007/s11269-011-9863-5

Cited by 10 publications

(5 citation statements)

References 22 publications

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“…Madani and Marino [ 54 ], applied a system dynamic framework to develop the Zayandeh-Rud Watershed Management and Sustainability Model (ZRW-MSM). Homayounfar et al [ 44 ], developed an annual non-discrete stochastic dynamic game model for reservoir operation and its corresponding solution was based on the collocation method. In this study, the logarithms of the 30-year monthly inflows to the reservoir were modeled with the Thomas-Fiering model.…”

Section: Resultsmentioning

confidence: 99%

“…In addition, according to the results, when compared with the annual dynamic game models, the presented models provide superior results. Indeed, the operating policies resulting from the second model are more practical than those of the annual models [ 42 , 44 ].…”

Section: Resultsmentioning

confidence: 99%

“…We employ the collocation method to solve this model. The presented model was developed based on a previous study by Homayounfar et al [ 44 ]. The presented model results in monthly operating policies distributing limited available water among different users using NBS.…”

Section: Introductionmentioning

confidence: 99%

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Two Monthly Continuous Dynamic Model Based on Nash Bargaining Theory for Conflict Resolution in Reservoir System

et al. 2015

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So far many optimization models based on Nash Bargaining Theory associated with reservoir operation have been developed. Most of them have aimed to provide practical and efficient solutions for water allocation in order to alleviate conflicts among water users. These models can be discussed from two viewpoints: (i) having a discrete nature; and (ii) working on an annual basis. Although discrete dynamic game models provide appropriate reservoir operator policies, their discretization of variables increases the run time and causes dimensionality problems. In this study, two monthly based non-discrete optimization models based on the Nash Bargaining Solution are developed for a reservoir system. In the first model, based on constrained state formulation, the first and second moments (mean and variance) of the state variable (water level in the reservoir) is calculated. Using moment equations as the constraint, the long-term utility of the reservoir manager and water users are optimized. The second model is a dynamic approach structured based on continuous state Markov decision models. The corresponding solution based on the collocation method is structured for a reservoir system. In this model, the reward function is defined based on the Nash Bargaining Solution. Indeed, it is used to yield equilibrium in every proper sub-game, thereby satisfying the Markov perfect equilibrium. Both approaches are applicable for water allocation in arid and semi-arid regions. A case study was carried out at the Zayandeh-Rud river basin located in central Iran to identify the effectiveness of the presented methods. The results are compared with the results of an annual form of dynamic 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 both models are capable of tackling conflict issues in water allocation in situations of water scarcity properly. Also, comparing the annual dynamic game models, the presented models result in superior results in practice. Furthermore, unlike discrete dynamic game models, the presented models can significantly reduce the runtime thereby avoiding dimensionality problems.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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Two Monthly Continuous Dynamic Model Based on Nash Bargaining Theory for Conflict Resolution in Reservoir System

et al. 2015

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“…This is where dynamic programming is of value. These techniques have been used in natural resources management and bioeconomic models (Ganji et al 2008, Homayounfar et al 2011, Alvarez et al 2016, Yaegashi et al 2017, Zhao et al 2017, Liu et al 2018, Anderies et al 2019.…”

Section: Introductionmentioning

confidence: 99%

Resilience-performance trade-offs in managing social-ecological systems

Homayounfar¹,

Muneepeerakul²,

Anderies³

2022

E&S

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Resilience-based approaches have been attracting attention in governing social-ecological systems facing rapid social and environmental changes. In this article, we investigate the governance policies that focus on resilience. Our analysis is built on a stylized dynamical model that mathematically operationalizes a widely used conceptual framework, which links social components, natural resources, and infrastructure in social-ecological systems. Specifically, we numerically solve the Hamilton-Jacobi-Bellman (HJB) equation to determine policies-in the form of investment in public infrastructure-that maximize a quantitative metric of the system's resilience. For comparison purposes, we also derive policies that maximize the system's performance and discuss the differences between and implications of the two policies. The results showed that a policy that maximizes performance results in sub-optimal resilience and vice versa. Moreover, our sensitivity analysis suggests that managing resilience requires that one be more responsive to changes in external forcing.

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“…One such common issue is that many of these models have been developed for a single reservoir system and cannot be easily adapted for use in multi-reservoir systems, mainly due to the “curse of dimensionality” (see [ 17 , 27 , 28 , 34 , 40 , 41 ]). Another issue is that many of these solutions do not consider the dynamicity of supply or demand components during optimization processes (cf [ 25 , 26 ]). Such models tend to take a static view of demand points while seeking to develop the optimum operation rules.…”

Section: Introductionmentioning

confidence: 99%

Development and application of coupled system dynamics and game theory: A dynamic water conflict resolution method

et al. 2017

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Conflicts over water resources can be highly dynamic and complex due to the various factors which can affect such systems, including economic, engineering, social, hydrologic, environmental and even political, as well as the inherent uncertainty involved in many of these factors. Furthermore, the conflicting behavior, preferences and goals of stakeholders can often make such conflicts even more challenging. While many game models, both cooperative and non-cooperative, have been suggested to deal with problems over utilizing and sharing water resources, most of these are based on a static viewpoint of demand points during optimization procedures. Moreover, such models are usually developed for a single reservoir system, and so are not really suitable for application to an integrated decision support system involving more than one reservoir. This paper outlines a coupled simulation-optimization modeling method based on a combination of system dynamics (SD) and game theory (GT). The method harnesses SD to capture the dynamic behavior of the water system, utilizing feedback loops between the system components in the course of the simulation. In addition, it uses GT concepts, including pure-strategy and mixed-strategy games as well as the Nash Bargaining Solution (NBS) method, to find the optimum allocation decisions over available water in the system. To test the capability of the proposed method to resolve multi-reservoir and multi-objective conflicts, two different deterministic simulation-optimization models with increasing levels of complexity were developed for the Langat River basin in Malaysia. The later is a strategic water catchment that has a range of different stakeholders and managerial bodies, which are however willing to cooperate in order to avoid unmet demand. In our first model, all water users play a dynamic pure-strategy game. The second model then adds in dynamic behaviors to reservoirs to factor in inflow uncertainty and adjust the strategies for the reservoirs using the mixed-strategy game and Markov chain methods. The two models were then evaluated against three performance indices: Reliability, Resilience and Vulnerability (R-R-V). The results showed that, while both models were well capable of dealing with conflict resolution over water resources in the Langat River basin, the second model achieved a substantially improved performance through its ability to deal with dynamicity, complexity and uncertainty in the river system.

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

Cited by 10 publications

References 22 publications

Two Monthly Continuous Dynamic Model Based on Nash Bargaining Theory for Conflict Resolution in Reservoir System

Two Monthly Continuous Dynamic Model Based on Nash Bargaining Theory for Conflict Resolution in Reservoir System

Resilience-performance trade-offs in managing social-ecological systems

Development and application of coupled system dynamics and game theory: A dynamic water conflict resolution method

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