School of Business, Hohai University, Nanjing, China.
International River Research Centre, Hohai University, Nanjing, China.
PLoS One. 2022 Jul 19;17(7):e0265350. doi: 10.1371/journal.pone.0265350. eCollection 2022.
The present work aims to find the optimal solution of Nash Equilibrium (NE) in the traditional Game Theory (GT) applied to water resources allocation. Innovatively, this paper introduces Particle Swarm Optimization (PSO) into GT to propose a cooperative game model to solve the NE problem. Firstly, the basic theory of the PSO algorithm and cooperative game model is described. Secondly, the PSO-based cooperative game model is explained. Finally, the PSO-based cooperative game model is compared with the Genetic Algorithm (GA) to test the performance. Besides taking the countries in Lancang Mekong River Basin as the research object, this paper discusses each country's water consumption and economic benefits under different cooperation patterns. Then, a series of improvement measures and suggestions are put forward accordingly. The results show that the average server occupancy time of the PSO-based cooperative game model is 78.46% lower than that of GA, and the average waiting time is 79.24% lower than that of the GA. Thus, the model reported here has higher computational efficiency and excellent performance than the GA and is more suitable for the current study. In addition, the multi-country cooperation mode can obtain more economic benefits than the independent water resource development mode. This model can quickly find the optimal combination of 16 cooperation modes and has guiding significance for maximizing the benefits of cross-border water Resource Utilization. This research can provide necessary technical support to solve the possible contradictions and conflicts between cross-border river basin countries and build harmonious international relations.
本研究旨在寻找传统博弈论（GT）在水资源分配中的纳什均衡（NE）的最优解。创新性地将粒子群优化（PSO）引入 GT 中，提出了一种合作博弈模型来解决 NE 问题。首先，介绍了 PSO 算法和合作博弈模型的基本理论。其次，解释了基于 PSO 的合作博弈模型。最后，将基于 PSO 的合作博弈模型与遗传算法（GA）进行比较，以测试性能。本研究以澜沧江湄公河流域国家为研究对象，讨论了不同合作模式下各国的用水量和经济效益。然后，提出了一系列改进措施和建议。结果表明，基于 PSO 的合作博弈模型的平均服务器占用时间比 GA 低 78.46%，平均等待时间比 GA 低 79.24%。因此，与 GA 相比，所提出的模型具有更高的计算效率和出色的性能，更适合当前的研究。此外，多国合作模式比独立水资源开发模式能获得更多的经济效益。该模型可以快速找到 16 种合作模式的最优组合，对实现跨境水资源利用效益最大化具有指导意义。本研究可为解决跨境流域国家可能存在的矛盾和冲突，构建和谐国际关系提供必要的技术支持。
