# Bargaining Power in Cooperative Resource Allocations Games
## 1 Introduction  
Cooperative game theory has been popular in the resource allocation literature to develop win-win agreements that lead to increased benefits for all parties This quantitative branch of game theory deals with problems in which cooperation can increase the total utility of all players [1]. In such problems, the main question is how to fairly and efficiently allocate the incremental benefits of cooperation to the parties such that they have incentives to resolve the conflict over utility sharing through cooperation. Cooperative game theory methods help answer this question by considering the incremental benefits of full and partial coalitions among players and their non-cooperative (status-quo) utilities [2]. With the growing competition over the scarce natural and environmental resources, decision makers can benefit from cooperative game theory methods to promote cooperation. This is one of the major motivations of the increasing use of cooperative game theory in the natural resource allocation literature [3; 4; 5; 6; 7; 8; 9; 10]. Cooperative game theory has also served a valuable framework to provide insights into transboundary water and environmental resources conflicts, project their future evolutions, identify their possible resolution, and design effective mediation strategies [11; 12]. [PERSON] and [PERSON] [13; 14] used cooperative (and non-cooperative) game theory to find possible resolutions for the Great Lakes dispute between Canada and the USA. [PERSON] and [PERSON] [15] applied cooperative game theory to suggest mechanisms to resolve conflicts in the western Middle Eastern water conflict in the Nile, Jordan, and the Tigris-Euphrates River basins. [PERSON] and [PERSON] [16] applied cooperative game theory to compare how cooperative and non-cooperative strategies affected consumable water availability in theJordan River Basin conflict. [PERSON] and [PERSON] [17] used cooperative game theory concepts to determine stable water allocation shares of Turkey, Syria, and Iraq in the Tigris-Euphrates transboundary river system. [PERSON] et al. [7] showed that cooperation and benefit sharing can lead to higher gains for all riparian countries in the Mekong River Basin. A pollution control study by [PERSON] et al. [18] suggested that the stakeholders' gain can be maximized through cooperation when they all agree to transfer a portion of their gain to cover the losses caused by pollution to other players. In a recent study, [PERSON] et al. [19] investigated the water allocation conflict among Turkmenistan, Afghanistan, and Iran over Harirud River. The authors concluded that cooperative reallocation of water can boost the stability of the cooperation among the countries. Cooperative game theory methods try to consider each player's value to each possible coalition of players to provide solutions that are potentially acceptable and seem fair to the conflict parties. They deal with what each player brings to the table or their endogenous powers in the benefit-sharing game. While considering the players' endogenous powers in a cooperative game is necessary for developing solutions, overlooking their exogenous powers might make the cooperative game theory solutions impractical. In real-world conflicts and bargaining processes, the negotiating parties also take advantage of the exogenous powers to the game (such as e.g., reputation, fame, popularity, track records, military, political and economic power) to alter the outcome in their favor and increase their gains. Nonetheless, the well-known and popular cooperative game theory methods do not account for the exogenous powers. Thus, in this study, we reformulate three well-known cooperative game theory concepts to show how the players' exogenous powers (weights) can be taken into account besides their endogenous powers in finding solutions to cooperative game theory problems.