An integrative case study approach between game theory and Pareto frontier concepts for the transboundary water resources allocations

Summary

In the context of transboundary issues, this paper introduces a composite water resources allocation approach that integrates both game theory and Pareto frontier concepts over the case of the Euphrates and Tigris Rivers. The proposed approach searches for an acceptable and viable solution set over the Pareto Frontier Surface via game theory based rationality constraints. For this purpose, the used base model is the Euphrates and Tigris River Basin Model, which is a linear programming model maximizing net economic benefits while optimally allocating scarce water resources in the basin. Results indicate that game theory based strategies and associated constraints provide a determinative backbone for an efficient and effective use of generated Pareto Frontier Surfaces. Additionally, estimated marginal values imply that the upstream countries have upper hand positions regarding their geographic and climatic contexts. After all the generation schemes, it appears that Turkey is the critical partner for inclusion into any form of coalition in the Euphrates and Tigris River Basin.

Introduction

As the world population increases and economy grows, the importance of clean water increases in the World, especially in the arid and semi-arid regions. Today, while observing the symptoms of global warming, transboundary water resources allocation has already entered into the academic and political discussions and analyses. It has also been a topic of hydrology especially when considering the globally changing spatial and temporal aspects of natural events, such as precipitation amounts, durations, frequencies, and intensities. Beyond the hydrologic aspects of the water resources issues, their allocations among the competing parties, not only in efficiency perspective but also in political and ecological ones, have been the topic of water related interdisciplinary scientific scope. Literature on transboundary water resources allocation can be classified into two broad categories: (i) descriptive studies covering wide spectrum of legal and political aspects of the topic and (ii) quantitative studies covering technical aspects of various allocation issues. This study can be categorized more on the quantitative and modeling aspects of the literature.

Quantitative studies also can be categorized into two groups. The first one is the basic quantitative modeling studies on the optimal and efficient allocation of scarce water recourses among multiple uses and parties. Though being not in the transboundary water resources literature, Flinn and Guise, 1970, Booker and Young, 1994, Mahan et al., 2002 and Becker (1995) have made significant contributions to the modeling aspects of similar issues. Flinn and Guise (1970) provided an initial example of optimization model for the allocation of scarce water resources via ‘Spatial Price Equilibrium and Linear Programming’ model developed by Samuelson (1952) and Takayama and Judge (1964) on a hypothetic river basin. Booker and Young (1994) utilized a non-linear model encountering various economic benefits (agriculture, urban, and energy), environmental issues, and an institutional framework of the international agreements between the USA and Mexico while allocating water resources among the USA states (Nevada, Arizona, Colorado, New Mexico, Utah, California). Mahan et al. (2002) developed a similar model based on principles outlined in Flinn and Guise (1970) for an actual water resources basin in the Southern Alberta. Becker (1995) utilized a linear programming model allocating scarce water resources for the Israeli regional crops considering value added of water, transfer costs, and basic system constraints (such as maximum reservoir supplies and agricultural areas). Among these literature mentioned above, Booker and Young (1994) outstands as a critical work which develops a model over an actual river (Colorado River), which is similar to the Euphrates and Tigris River Basin (ETRB).

The second one is the game theory based allocation studies considering behaviors of competing and conflicting parties over the transboundary water resources. One of the earliest game theory based transboundary water resources allocation model dates back to 1969 by Rogers (1969) with his studies on the Ganges. Later in 1993, Rogers (1993) outlined the basic modeling concepts (Pareto frontier, game theory) that can be used for the allocation of scarce water resources. Dinar and Wolf (1994a) and Wu and Whittington (2006) studied the Middle East- North Africa water problems such as the Nile River. Dinar and Wolf (1994a) designed cooperative and non-cooperative allocation models for the Nile water among Egypt, Israel, West Bank, and Gaza Strip and evaluated them for the approval of the relevant parties via Political Accounting System (PAS). Similar to Kucukmehmetoglu and Guldmann, 2004, Wu and Whittington, 2006 pursued an allocation study by focusing on cooperative game theory concepts, such as core and Shapley. In their study, the case area was the Nile Basin and the techniques were core and nucleolus games, and generalized Shapley value to attain baseline conditions for incentive-compatible solutions. Kampragou et al. (2007) and Eleftheriadou and Mylopoulos (2008) worked on the River Nestos/Mesta. While Eleftheriadou and Mylopoulos (2008) were applying game theory concepts in the allocation of scarce water resources between Bulgaria and Greece, Kampragou et al. (2007) developed a model using weighing factors for an equitable and reasonable allocation of water resources based on international legislation, which are the UN guidelines and the EU Water Framework Directive. Recently, Teasley and McKinney (2011) presented an interesting work on the Syr Darya Basin allocating water resources between the basin countries by considering the conflicting seasonal energy and agricultural demands. The Draft Agreement in 1998 on the timing of allocation was analyzed by means of various allocation techniques including cooperative game theory concepts. Madani (2010), after an extensive literature review, dwelled on various two-player non-cooperative games (such as prisoner’s dilemma, stag-hunt, and chicken game) in an evolutionary perspective (dynamic games) to present the varying game strategies over a sequential 4-period. In the analyses, he used Pareto optimality, Nash equilibrium, and dominant strategy concepts to present the changes in the nature of strategies.

Kucukmehmetoglu, 2002, Kucukmehmetoglu, 2009, Kucukmehmetoglu et al., 2010 and Kucukmehmetoglu and Guldmann, 2004, Kucukmehmetoglu and Guldmann, 2010 have pursued research on the Euphrates and the Tigris Rivers. In the earlier modeling studies, it is found that grand coalition, in which all involved parties behave as if they are under a single authority and utilize all resources efficiently without entailing any privileges to anyone, provides the highest net economic benefits as compared to the sum of various forms of sub-coalition and individual benefits (Kucukmehmetoglu and Guldmann, 2004). In this process, many cooperating parties may be required to give up unilateral or subgroup benefits for the higher total net economic benefit at the grand coalition. However, at the grand coalition (or global optimization), disadvantageous parties (often, but not necessarily, the upstream country) need to be compensated from the grand coalition benefit or from an outside source as a subsidy. Grand coalition result by itself does not provide sufficient information to attract disadvantaged parties. In the earlier studies, in order to solve this, the focus was on (i) the game theoretic aspects of the transboundary water resources allocation (Kucukmehmetoglu and Guldmann, 2004) and (ii) the generation of trilateral Pareto frontier tradeoff surface (where all basin resources are optimally used and any county’s increase in benefit results in corresponding decreases in the benefits of the other two counties) among the basin countries to be able to determine an intelligent allocation scheme via additional constrained optimization operations reflecting subjective political desires of involved parties (Kucukmehmetoglu and Guldmann, 2010). Through the combination of these two approaches, this study makes some elaborations on (i) selection of the valid and strategically attainable extent of Pareto frontier tradeoff surface that countries can actually compete and (ii) determination of the necessary amount of compensation to attract or convince the influential and influenced parties to take part in the grand coalition. In the analyses, cooperative game theory based strategies are used to determine workable tradeoff surface and country net economic benefits, marginal impacts and their ranges (min–max). Kucukmehmetoglu (2009) and Kucukmehmetoglu et al. (2010) are among the other studies contributing to the literature by the game theory applications focusing on, respectively, (i) the impacts of built infrastructures (reservoirs) on the basin-wide coalition formations under varying water flows scenarios and (ii) the allocation of extra benefits driven from grand coalition among the multiple parties via fuzzy logic concepts especially for the uncertain subjective political and volatile natural environments.

Although extensive academic research has been conducted, allocation of scarce water resources remains as an issue to be solved in the world. So far, an agreed framework is yet to be developed due to the unique and complex characteristics of each basin. Every basin has accumulated geological, geographic, historic, social, and economic characteristics that may require specific treatments without any fit into a generic legal and procedural framework.

This study provides the results of dual solutions of the Euphrates and Tigris River Basin Model (ETRBM) via the General Algebraic Modeling System (GAMS). The proposed methodology finds out the necessary marginal values of decision constraints. These marginal values show the impact measurements of individual country or a sub-group of countries on the grand net economic benefits.