基于多线性扩展的模糊双合作博弈的支付分配策略模型

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

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.

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 exten- sion 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 prop- erty, 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.