Free-Ride and Equilibriums in a Cooperative Game of Cascade Reservoirs
Publication: Journal of Water Resources Planning and Management
Volume 150, Issue 9
Abstract
The cooperative operation of cascade reservoir systems is an efficient way to regulate water resources. However, noncooperation among various reservoir stakeholders is often observed in practice; this produces an interesting dilemma in the game of water resource management. Considering the upper Yellow River cascade reservoir system as a case study, in this paper we model and analyze the cooperation dilemma in a cascade reservoir system. In our game theoretical analysis, we find that, except for the most upstream reservoir, all reservoirs have free-ride strategies. The free-ride strategy indicates that a reservoir obtains free gain from the cooperation of other reservoirs due to spatial connections, and this fact changes the cooperative game in terms of equilibrium and benefit allocation. The results show that the regulation capacity of the free rider directly affects the equilibrium and benefit allocation of the game. A midstream reservoir with a small or medium regulation capacity tends to employ a free-ride strategy. A midstream reservoir with a large regulation capacity can entirely interrupt the cooperation between upstream and downstream reservoirs, interestingly, which can lead to the disappearance of the free-ride strategy for the midstream reservoir. However, the downstream reservoir may employ a free-ride strategy when the midstream reservoir chooses to cooperate. This implies that grand cooperation is not stable when considering free-ride, whereas partial coalitions are more likely to form. In this paper, we derive equilibrium in the cooperative game of cascade reservoirs, providing theoretical interpretation of the noncooperation phenomenon in the operation of cascade reservoirs.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This research was supported by the National Natural Science Foundation of China (U2243215 and 42041004) and National Key Research and Development Program of China (Grant No. 2021YFC3201204).
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Journal of Water Resources Planning and Management
Volume 150 • Issue 9 • September 2024
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© 2024 American Society of Civil Engineers.
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Received: Dec 8, 2023
Accepted: Apr 3, 2024
Published online: Jul 13, 2024
Published in print: Sep 1, 2024
Discussion open until: Dec 13, 2024
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