# Bargaining Power in Cooperative Resource Allocations Games
## 6 Conclusions  
This study aimed to adapt and reformulate cooperative game theory methods to include players' exogenous negotiating powers to develop cooperative solution for real-world games. The study was motivated by the idea that considering the bargaining power of the decision makers can better capture the complexity of real-world games and would lead to more feasible path to conflict resolution [51]. We reformulated the Nash-Harsanyi, Shapley, and Nucleolus methods and applied to them ongoing Caspian Sea negotiation between five littoral states. Based on the study results, the Condominium governance regime or any other mechanism that results in equal shares for all players is potentially acceptable. When the players' bargaining powers based on various economic, military, and political factors are considered, the countries' cooperative shares varied between a high of 37% for Russia to a low of 12% for Turkmenistan. The study also reformulated two commonly used methods for evaluating the potential acceptability and stability of cooperative solutions in cooperative games with asymmetric bargaining powers. The stability analysis results suggest that resource allocation based on the Nash-Harsanyi solution has the highest potential degree of stability and acceptability.  
The study results suggest that new allocation solutions that have not been considered in the negotiations can help the Caspian Sea conflicts reach a resolution. Future studies can use the Caspian Sea NSS [43] to explore how the potentially acceptable game theoretic allocation solutions can be implemented in practice by developing optimal geographical boundaries.  
Conceptualization, K.M.; methodology, K.M. and F.F.; validation, K.M. and F.F.; formal analysis, K.M. and F.F.; investigation, K.M.; resources, K.M. and F.F.; data curation, F.F. and S.G.; writing--original draft preparation, K.M.; writing--review and editing, K.M. and F.F.; visualization, S.G.; supervision, K.M. All authors have read and agreed to the published version of the manuscript.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Scenario 1**} & \multicolumn{3}{c}{**Scenario 2**} & \multicolumn{3}{c}{**Scenario 3**} \\ \hline
**N-H** & **Nucleolus** & **Shapley** & **N-H** & **Nucleolus** & **Shapley** & **N-H** & **Nucleolus** & **Shapley** \\ \hline
0.01 & 0.01 & 0.003 & 0.06 & 0.05 & 0.02 & 0.06 & 0.05 & 0.02 \\ \hline \hline \end{tabular}
\end{table}
Table 6: The power index of the proposed solutions under different scenarios.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Country**} & \multicolumn{3}{c}{**Scenario 1**} & \multicolumn{3}{c}{**Scenario 2**} & \multicolumn{3}{c}{**Scenario 3**} \\ \cline{2-10}  & **N-H** & **Nucleolus** & **Shapley** & **N-H** & **Nucleolus** & **Shapley** & **N-H** & **Nucleolus** & **Shapley** \\ \hline Azerbaijan & 0.998 & 0.997 & 0.997 & 0.998 & 0.959 & 0.965 & 0.998 & 0.959 & 0.965 \\ Iran & 1.003 & 1.000 & 1.001 & 1.003 & 1.022 & 1.017 & 1.003 & 1.022 & 1.017 \\ Kazakhstan & 0.998 & 1.021 & 1.017 & 0.999 & 1.070 & 1.056 & 0.999 & 1.070 & 1.056 \\ Russia & 1.000 & 0.987 & 0.988 & 1.001 & 0.938 & 0.948 & 1.001 & 0.938 & 0.948 \\ Turkmenistan & 0.999 & 1.007 & 1.007 & 0.999 & 1.094 & 1.083 & 0.999 & 1.094 & 1.083 \\ \hline \hline \end{tabular}
\end{table}
Table 7: The propensity to disrupt for the game theoretic solutions under different scenarios.  
**Funding:** This research received no external funding.  
**Data Availability Statement:** Not applicable.  
**Acknowledgments:** The authors are thankful to [PERSON], [PERSON], [PERSON] and other members of the Hydro-Environmental and Energy Systems Analysis (HEESA) Group at the University of Central Florida (UCF) for their help, feedback and input.  
**Conflicts of Interest:** The authors declare no conflict of interest.