多主体水库群联合调度增益分配讨价还价模型

建立公平、高效、合理的增量效益分配机制是促进多利益主体水库群开展联合优化调度的关键。基于上述原则，提出基于讨价还价理论的增量效益分配模型。采用一阶最优性条件推导模型最优解，发现最优效益分配方案满足主体效用函数拟微增率相等的条件。与基于比例分配法、Shapley模型的分配方案比较，结果表明：（1）讨价还价模型分配方案与各主体的效益分配区间和子联盟约束力有关。若子联盟效益贡献低，约束力小，主体增量效益与其效益分配区间正相关；若子联盟效益贡献高，约束力大，子联盟内成员的分配效益将优先保证。（2）各分配方案的差异源于公平性定义方式的差别。（3）讨价还价模型分配的增量效益方案趋均化程度最高，保障了弱势主体既得利益。

Bargaining model of allocating incremental benefit from joint operations of multi-stakeholder reservoir system

Establishing a fair, efficient and reasonable mechanism of allocating incremental benefit is the key to enhancing optimal joint operations of a multi-reservoir system owned by multiple stakeholders. Based on this principle, an incremental benefit allocation model is developed in this study using the bargaining theory. We derive optimal solutions of the model using the first-order optimality condition, and reveal that the optimal benefit allocation plan meets the conditions of equivalent quasi-slope on each stakeholder’s utility function. Compared to the allocation plans based on the proportional allocation model and Shapley model, the results show that allocation plans of this bargaining model are determined by the interval of each stakeholder’s benefit distribution and the effectiveness of sub-coalition constraints. If the benefit contribution of the sub-coalition is low, the incremental benefit allocated to a stakeholder is positively correlated with its interval of benefit allocation, while when this contribution is high, a high priority will be granted to allocating the excessive benefits of the reservoirs within the sub-coalition. The differences among various methods are generally influenced by how the equality is defined. The incremental benefit allocation plan generated by the bargaining model is highly homogenized to all the reservoirs, and thus ensures the benefit of those weak stakeholders.