Game Theory Applications in a Water Distribution Problem

Abstract

<p align="justify"> <span style="font-family:Verdana;font-size:10pt;">A water distribution problem in the Mexican Valley is modeled first as a three</span><span style="font-family:Verdana;font-size:10pt;">-</span><span style="font-family:Verdana;font-size:10pt;">person noncooperative game. Each player has a five</span><span style="font-family:Verdana;font-size:10pt;">-</span><span style="font-family:Verdana;font-size:10pt;">dimensional strategy vector, the strategy sets are defined by 15 linear constraints, and the three payoff functions are also linear. A nonlinear optimization problem is first formulated to obtain the Nash equilibrium based on the Kuhn-Tucker conditions, and then, duality theorem is used to develop a computational procedure. The problem can also be considered as a conflict between the three players. The non-symmetric Nash bargaining solution is suggested to find the solution. Multiobjective programming is an alternative solution concept, when the water supply of the three players are the objectives, and the water authority is considered to be the decision maker. The optimal water distribution strategies are determined by using these solution concepts and methods.</span> </p

Seeking a strategic cross boundary solution to the Indus Water basin sharing decisions

“…To account for the underlying asymmetries, the Asymmetric Nash Bargaining Solution (ANBS), which is the extension of the Nash Bargaining Solution, stands out as the prime solution concept as it take into account the asymmetries through bargaining weights (Giménez‐Gómez, Osório, & Peris, 2015). It has proved its significance to balance the utilities among the riparian involved and has been frequently used to address the river sharing issues (Ahmadi & Moreno, 2013; Ambec & Sprumont, 2000; Fu et al, 2018; Houba, Do, & Zhu, 2013).…”

Asymmetric Bargaining Model for Water Resource Allocation over Transboundary Rivers

“…The Nash bargaining solution has a strong potential to find win–win solutions for sharing water resources and their benefits since they can capture well coalitional dynamics [23,41], and has the ability to take most of the desirable properties of the river-sharing problem into account [9]. As river-sharing problems in reality have asymmetric attributes, the ANBS [65] has attracted considerable attention from water resource scientists, and has achieved remarkable results in some river conflicts including the Mekong River Basin [52], the Mexican Valley [53], the Huai River Basin [50], and the Aharchay River Basin [47]. Nevertheless, most of these studies make excessive assumptions about actual examples, especially in determining BWs.…”

“…Agent’s disagreement utility is the lower bound or starting point for his participation in bargaining [54], which, to some extent, determines the fairness and sustainability of existing treaties or agreements [51]. Therefore, the ANBS depends upon agents’ DUPs [47,51]. The agents’ gains in status quo are always directly used as their DUPs, but such gains may not exist in actual bankruptcy problems [31], and likely result in erroneous results [53] even if they do exist.…”

“…It has proved to be able to significantly balance the utilities among parties involved [44], and can serve as a base for sustainable river water-sharing agreements [45]. Hence, it is frequently used in the water resources literature [3,9,12,23,29,32,44,46,47,48,49,50,51,52,53,54] to address river-sharing issues involving multiple local decision makers that require consideration of the reliability criterion.…”

Energy Optimization and Cost Reduction in Water Distribution Networks

“…An investigation using numerical methods is being carried out at the Bupyeong 2 reservoir catchment in Incheon, Korea. In [8], the issue with the water distribution in the Mexican Valley was considered. In order to obtain the Nash equilibrium of the three-player game involving water users, one must first resolve a special quadratic optimization problem with linear constraints.…”