模糊支付合作博弈的可信性准核仁

合作博弈是处理局中人之间协同行为的数学理论。有诸如核心、稳定集、沙普利值、准核仁和核仁等不同的解概念。在很多情形,除了借助专家经验和主观直觉,没有恰当的方式来确定支付函数,由此产生了具有模糊支付的合作博弈模型。准核仁是一种重要的解概念,在模糊支付合作博弈中如何恰当定义准核仁是个重要的问题。本文在可信性理论的框架下研究了这个问题,定义了两类可信性准核仁概念并证明了它们的存在性和唯一性,同时研究了可信性核心、可信性核仁与它们之间的关系。

Credibilistic Prenucleolus of Cooperation Game with Fuzzy Payoffs

Cooperation game deals with situations that involve coordination or collaboration among the players. There are different solution concepts such as core,stable set,Shapley value,prenucleolus and nucleolus. In many situations, there is no way to predict the payoffs except for the expert experiences and subjective intuitions, which leads to the cooperation game with fuzzy payoffs. Prenucleolus is an important solution concept, how to define prenucleolus solution of cooperation game with fuzzy payoffs is left as an open question. This paper investigates this problem, within the framework of credibility theory, two definitions of credibilistic prenucleolus are proposed and their existence and uniqueness are proven. Meanwhile, the relationship between credibilistic core and credibilistic prenucleolus has been investigated.