Abstract
Given the institutional limitations of multi-stakeholders, exploring the synergistic revenue from the joint reservoir operations of a multi-stakeholder multi-reservoir system requires a synergistic revenue allocation mechanism to ensure a beneficial solution for multi stakeholders. This study established a synergistic revenue allocation model using bargaining game theory under the principles of equity, rationality, and efficiency. For the maximization the Nash product of gains in the utility of stakeholders and constraints on the feasibility of allocation plans considering all the possible formations of sub-coalitions, the analytic optimal solution of the bargaining model was derived using the first-order optimality condition. The optimal revenue allocation plan meets the conditions of the equal quasi-marginal utility function among stakeholders. The methodologies were applied to a hypothetical cascade reservoir system operated by multiple stakeholders. Compared with the revenue allocation plans obtained by a proportional rule method and the Shapley value method, the results corroborate that (1) the allocation plan of the bargaining model is jointly determined by the interval of the revenue range of each reservoir and the effectiveness of the sub-coalition constraints, indicating that the allocated synergistic revenue is positively correlated with the singleton contribution and team contribution on the total revenue of the grand coalition; (2) the difference in the plans obtained by the three methods is generally determined by the difference in equity definition; and (3) the synergistic revenue allocation plan obtained from the bargaining model is the highest homogenized among all reservoirs (stakeholders), which demonstrates that the revenue of those dominated stakeholders can be improved compared with other plans. The proposed methodologies provide new insights to guide benefit share decisions in multi-stakeholder reservoirs system.
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Acknowledgements
We would like to thank two anonymous reviewers for their in-depth reviews and constructive suggestions. The remarks and summary of reviewer comments provided by the Editor and Associate Editor are also greatly appreciated, which have facilitated major improvements in this paper. The authors are grateful to Dr. Yenan Wu for the help on revising the manuscript.
This study is supported by the National Key Technologies R&D Program of China (Grant No. 2017YFC0405604), the National Natural Science Foundation of China (Grant No. 51609062), the Fundamental Research Funds for the Central Universities (Grant No.2018B10514), and the China Postdoctoral Science Foundation Funded Project (Grant No. 2018T110525).
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Xu, B., Ma, Y., Zhong, Pa. et al. Bargaining Model of Synergistic Revenue Allocation for the Joint Operations of a Multi-Stakeholder Cascade Reservoir System. Water Resour Manage 32, 4625–4642 (2018). https://doi.org/10.1007/s11269-018-2075-5
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DOI: https://doi.org/10.1007/s11269-018-2075-5