Analysis and comparison of strategies the construction of short dams inside a catchment, and the construction of a long dam at the end of a catchment by application of game theory

Today, the calculation of sub-basin water balance is the most widely used application of game theory (Andik & Niksokhan 2020; Zarei et al., 2019). This study examines the hypothetical efficiency of game theory in determining the number of dams and distribution reservoirs. Simultaneous consideration of environmental, technical-economic and social criteria in formulating three different strategies is one of the innovations of the method for testing this hypothesis.

According to the topographic conditions and river network conditions, TAHAM area - 5763IV IRAN - located in Zanjan province was selected. Then, different basins were identified in the selected area and the largest basin was selected in terms of area and completeness of the waterway network. The number of strategies in this study is based on the hydrological classification of rivers. Therefore, the strategies were explained according to the classification of rivers within the main basin. This was done by dividing the basins based on categories two, three, four and five. However, due to the fact that the area of ​​first class river basins was very small, the division of basins into first class basins was not included. The following strategies are obtained based on the classification of rivers: (a) -Strategy S1: main basin with main river category five; (B) -Strategy S2: Divide the main basin into two sub-basins S2-1 with classification of river category three and sub-basin S2-2 with class four; (C) -Strategy S3: Division of S2 strategy basins into three sub-basins with three classifications, named S3-1, S3-2 and S3-3 and (d) -Strategy S4: Division of S3 strategy basins To sub-basins with two river categories, named S4-1, S4-2, S4-3, S4-4, S4-5, S4-6, S4-7 and S4-8.

After explaining and parameterizing the game rule, the outcome matrix of each game was obtained. Finally, according to the outcome matrix study, S2 strategy was identified as the Nash equilibrium or the answer to the problem. In this form, numbers are in tension and competition with each other. Simultaneously examining the criteria and consequences of adopting any strategy for each player practically creates interactions of effects and conflict of interest for the economic, social and environmental players. Examining the even matrix for three players with different choices can easily provide a very small change of consequences according to final results of models.

By using the game theory while solving concurrency and considering the damages caused by dam construction for the parameters (economy, environment, and community) regarding AHP model (which is based on scoring the damages and summing them) an alternative method was introduced.