基于多线性扩展的模糊双合作博弈的支付分配策略模型

针对参与联盟的局中人具有一定参与度的情形,研究了具有模糊联盟的双合作博弈的支付分配问题.首先,给出双合作博弈支付分配方案的一般化形式;其次,提出一种由双合作博弈扩展到模糊双合作博弈的多线性扩展形式,进而给出模糊双合作博弈的支付分配策略,并说明该支付分配方案满足有效性、零元性、哑元性、联盟内部对称性、联盟间对称性和单调性;最后,通过成本分摊算例,验证了模糊双合作博弈支付分配模型的可行性.

Model of payoff allocation for bi-cooperative game with fuzzy coalitions based on multilinear extension

Under the assumption that players do not fully participate in the cooperation, but to some extent, this paper studied the problem of payoff allocation for bi-cooperative game with fuzzy coalitions. First, the generalized payoff allocation is proposed for bi-cooperative game. Then, an multilinear extension form from bi-cooperative game to bi-cooperative game with fuzzy coalition is proposed. The payoff allocation model is constructed for bi-cooperative game with fuzzy coalitions. Furthermore, it proves that the payoff allocation satisfies some properties, such as efficiency, null player property, dummy player property, symmetric within coalitions, symmetric across coalitions, monotone property and so on. Finally, an example for cost distribution is provided to illustrate the feasibility of the developed method.