Abstract: Aiming at the problem that the Selectope contains too many imputation vectors which make it difficult for decision makers to focus on the final choice, this paper is focused on the imputation of cooperative games. Firstly, this paper sets the Selectope as the feasible region, which is obtained with the idea of assigning the Harsanyi dividends to players. Secondly, under the condition of completely rational player, this paper constructs an expression to describe the maximum player satisfaction with the idea of excess and the original intention of players being fully considered, and uses it as the objective function. Then a non-linear programming model based on the Selectope and the idea of the maximum player satisfaction is created to get the imputation mapping. At last, a numerical example is given to verify the feasibility of this idea and the rationality of the results. The conclusion shows that the method proposed in this paper can effectively reduce the volume of the Selectope, providing a concise choice space to decision makers. This research expands the application of the Selectope solution set to an extent, and the expression for the maximum player satisfaction constructed in this paper would achieve a reference value for future research.

Key words: cooperative game, player satisfaction, Selectope

摘要： 针对决策者在获取Selectope解集后难以聚焦到最终分配方案上的问题,论文对合作对策的解集进行了研究。首先借助Harsanyi红利在局中人中进行分配的思想,得到Selectope解集作为研究问题的可行域。之后,在局中人完全理性的条件下,充分考虑局中人参与合作的初衷,运用超出值的概念,构建了描述局中人最大满意度的目标函数,进而得到基于Selectope解集与局中人最大满意度的非线性规划模型,用于合作对策收益分配问题的求解。最后,通过算例验证了该求解思路的可行性与求解结果的合理性。研究结果表明,论文提出的求解思路能够有效缩减Selectope解集的体量,为决策者提供一个精炼的抉择空间,在一定程度上拓展了Selectope解集的应用,同时,构建的局中人最大满意度的非线性函数对局中人满意度研究也有一定的参考价值。

关键词: 合作对策, 局中人满意度, Selectope解集