Application of the Multi-objective Game Theory Model in Determining the Economic-Environmental Balance in Zrebar Lake watershed in Marivan

One of the most important challenges facing watershed management is the conflict between economic benefit of stakeholders and environmental protection in watersheds that in turn causes many problems such as land use change by stakeholders to increase profit, regardless of watersheds health problems. In this study, a multi-objective game theory (MOGT) model was developed as an alternative tool for resolving strategic conflicts, namely economic development (development and land use) and environmental protection (water quality preservation and reduction of pollutants) that was developed to decision making and balance the economic-environmental challenges of the Marivan Zrebar Lake watershed in Kurdistan province. Geographic information system (GIS) has been used to calculate and display different types of land uses. In this study, the environmentalists (player 1) and Zrebar basin users (player 2) were selected as environmental and economical players, respectively. The results of multi-objective game-theory model indicated that Nash equilibrium was established after seven rounds of bargaining and moderating the objectives between players and the balance between environmental and economic concerns in watershed management was established. Nash equilibrium varies for environmental actor ranges from 25365 to 25366 kg/ha and income for economic actor from 420 to 421 million Rials per year. The results also indicated that solving the multi-objective decision making model for the lake watershed does not result in a Pareto optimal, but rather a range of solutions. By comparing the results of the classical multi-objective planning model and the game theory based on rounds of bargaining, the MOGT model is superior to the clasical multi-objective model and can provide more satisfactory solutions based on decision makers' preferences. Findings of this research can be useful for land use change management in the watershed where there is conflict between economic and environmental concerns.     Extended Abstract

       Decision makers often have difficulty adopting the appropriate choice from among sundry uses of a watershed (Madani, 2010). Decision making is highly controversial due to conflicting criteria (Lee & Chang, 2005); in view of the fact that each user's behavior with different views, values, and interests also affects the choice and interests of others (Shields et al, 1999). Of discussions related to watershed management, there has been dispute concerning economic revenues from land development (deforestation, agriculture and recreational activities), environmental objectives (pollution reduction) and socio-economic plans (soil and water conservation) (Lund & Palmer, 1997). Looking at it from a scientific point of view, most of this controversy has focused on finding the pareto optimal solution (Madani, 2010). In other words, there must be a balance between increasing economic profits and reducing negative environmental impacts. In situations where objectives contradict each other, improvement regarding one goal is achieved at the cost of overlooking another goal or reducing the likelihood of achieving it (Raquel et al, 2007). Among methods aim at tackling such issues in conflict situations is the multi-objective model of game theory.

   In this study, as the first step, a linear optimization model with two economic and environmental objectives was developed to maximize the profit of the users living next to the Zrebar Lake basin and to minimize the environmental pollution of the lands around (conventional model). The optimal solution of the pareto is obtained via employing this model. From an economic point of view, in order for the lands in a watershed to generate maximum income, they must be allocated to different uses. On the other hand, from an environmental point of view, watershed lands should not be exploited more than their respective capacity range. At this stage, the contradiction between economic and environmental objectives is clearly visible; because the nature of Pareto's optimal solution is such that any improvement with respect to one objective is achieved simply by degrading one other objective. As the second step, in order to resolve the conflict between economic and environmental objectives, they confront one another, and Nash equilibrium will be established through the bargaining process (game model). The Nash equilibrium feature attained from the algorithmic bargaining process ensures that each player has made the best decision against the constraints imposed by the second player. The essential data were collected by segregation of the region based on different uses of the land of the watershed, using the Geographic Information System (GIS), and the plans made in the Zrebar watershed during 2015-2016. In order to solve the multi-objective decision problem, the ArcGis Desktop 9.0 software package was used to extract accurate data.

        In the present study, for the economic player, the goal was to maximize income, which includes agricultural, horticultural, tourism-recreational, industrial and animal husbandry activities. For the second player, the minimum concentration of phosphorus and nitrogen was considered as the environmental objective. First, each player identifies the maximum and minimum values by analyzing the single-objective function. The primary objective for the first player (environmental player) equals the lowest possible pollution level of EnvPmin = 19840 kg per hectare per year, while the primary objective for the second player (economic player) is to earn the highest possible income, ie EcoDmax =56500000  Rials per hectare per year. Since the initial results of the simulation of the multi-objective model are not satisfactory with respect to each player, both entered the first round of negotiations. During the bargaining process, players moderate their objectives. The strategy of the first player was set to increase from 20,000 to 25,365 kilograms per hectare, and the strategy of the second player was set to decrease from 54 to 42.1 million rials per hectare. The greater the difference between the values shown and the values obtained from the optimization process, the closer to the real equilibrium point. After the seventh round of bargaining, the value of EnvP = 25365 obtained by solving the mathematical programming model is approximately equal to the value determined by the environmental player, and the EcoD value is approximately equal to the value determined by the economic player. The results at this stage are satisfactory for both players and therefore they reached the Nash equilibrium point.

          The current study aimed at evaluating the feasibility of using the multi-objective Game Theory (MOGM) model to fashion a balance between economic and environmental challenges in optimizing land use in the watershed of Zrebar Lake in Marivan and to help ease the decision-making process. Supporters and advocates for environment and forests protection were selected as the first player (environmental player) and users of the Zrebar Lake watershed as the second player (economic player). The results indicated that:Using the multi-objective decision-making model for the lake's watershed has not led to an optimal solution of the Pareto, but to a range of solutions.In the game model, each player takes actions for his personal interests, but in the conventional multi-objective model, players take initiative to improve the interests of the whole system. What is more likely to happen in the real world is that people prefer personal interests to collective ones. Overfishing, poaching, excessive water pumping, illegal well drilling, etc. are all considered reasons for the benefit of individualism in the real world. Nash equilibrium will scientifically describe such behavior.In balance mode, the level of cultivation of crops like wheat and barley was constant, but garden products, summer crops, vegetables and straw-covered fields have been removed from the model. This indicates that these kinds of activity have not been compatible with environmental objectives.By comparing the results of the conventional multi-objective programming model and the game model based on bargaining rounds, the superiority of the MOGT model was confirmed over the conventional multi-objective programming model. Therefore, it is recommended to consider the best measures affecting water quality and increasing income, such as replacing the new source of livelihood, reducing the use of fertilizers, replacing vegetable and fruit cultivation instead of wheat.