A fuzzy game theoretic approach for groundwater resources management: Application of Rubinstein Bargaining Theory

Abstract

Developing optimal operating policies for conjunctive use of surface and groundwater resources when different stakeholders with conflicting objectives are involved, is usually a challenging task. This problem would be more complex when objectives related to surface and groundwater quality are taken into account. In this study, a new methodology is proposed to resolve the conflict of interests among water users, water supply and environmental protection agencies which are involved in a problem of conjunctive use of surface and groundwater resources.

In order to develop a Pareto front among objectives, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) is used. To incorporate the objectives related to groundwater table fluctuations and groundwater quality, the MODFLOW and MT3D groundwater quantity and quality simulation models and the optimization model are embedded. The best non-dominated solution on the Pareto front is selected using the Rubinstein Sequential Bargaining Theory (RSBT). The Fuzzy Set Theory is also utilized to better define the utility functions of decision makers. To evaluate the efficiency of the proposed methodology, it is applied to the conjunctive use of surface and groundwater resources in the Tehran metropolitan area, Iran.

Introduction

Conjunctive use of surface and groundwater resources is a water management practice which combines the use of both sources of water in order to minimize the undesirable physical, environmental and economic effects of each use on the other and maximizes the net benefits from them over time. Since different stakeholders with conflicting preferences are usually involved in conjunctive use of surface and groundwater resources, developing optimal conjunctive use policies is a challenging task.

In conjunctive use problems, the Pareto front among different conflicting economic and environmental objectives can be determined using Multi-Objective Evolutionary Algorithms (MOEAs), which can reduce the computational burden of the classical multi-objective decision making techniques. The Non-Dominated Sorting Genetic Algorithm (NSGA) proposed by Srinivas and Deb (1995) was one of the first MOEAs. Over the years, the main shortcomings of the NSGA have been demonstrated which are fully described by Deb (2001) and Deb et al. (2002). To overcome the drawbacks of NSGA, its new version called NSGA-II was proposed by Deb et al., 2000, Deb et al., 2002. The NSGA-II, which is used in this study, employs both elitism approach and a crowd comparison operator that maintains diversity among chromosomes in each population.

Applications of NSGA-II include watershed management (Dorn and Ranjithan, 2003), groundwater quality monitoring (Reed et al., 2003, Reed and Minsker, 2004), water distribution system design (Kapelan et al., 2005) and river water quality management (Yandamuri et al., 2006, Niksokhan et al., 2009a).

The best non-dominated solution on the Pareto front can be selected using a bargaining theory. In the past decades, different game and bargaining theories have been presented by economists. In recent years, these theories have been applied to some problems in the filed of water resources and environmental systems management. For example, Kerachian and Karamouz, 2006, Kerachian and Karamouz, 2007 proposed two methodologies for water quality management in reservoirs and river–reservoir systems. They used the Nash bargaining theory in order to include conflicting interests of different stakeholders in river–reservoir systems.

Salazar et al. (2007) used four different conflict resolution methods, namely non-symmetric Nash solution; non-symmetric Kalai–Smorodinsky solution; non-symmetric area monotonic solution and non-symmetric equal loss solution to find the best groundwater extraction scenario among different alternatives. Shirangi et al. (2008) used the Young Conflict Resolution Theory (YCRT), to develop reservoir operating rules considering the water quality issues.

Mahjouri and Ardestani (2009) proposed a new game theoretic methodology for interbasin water transfer management with regard to economic, equity, and environmental criteria. In their methodology, the water and benefit are reallocated to stakeholders using some cooperative games. Niksokhan et al. (2009b) developed a methodology for cooperative pollutant discharge permit trading in rivers considering the conflict of interests of decision makers and stakeholders.

A conflict resolution model was proposed by Bazargan-Lari et al. (2009) for conjunctive use of surface and groundwater resources. They used the YCRT to resolve the existing conflict among stakeholders and presented the water allocation policies. They assumed that the utility functions of stakeholders are precisely available.

In this study, a fuzzy version of the methodology presented by Bazargan-Lari et al. (2009) is developed for conflict resolution in conjunctive use of surface and groundwater resources considering the water quality issues. The Rubinstein Sequential Bargaining Theory (RSBT), which considers the stakeholders’ patience, is used for modeling the bargaining process among stakeholders. The existing uncertainties in the utility functions of stakeholders are also incorporated using the α-cut method in Fuzzy Set Theory. To evaluate the efficiency and applicability of the methodology, it is applied to Tehran aquifer in the Tehran metropolitan area, Iran.