联盟缺额合意性与均分不可分贡献值

Coalitional Gap Desirability and the Equal Allocation of Non-Separable Contributions Value

文章首先基于联盟盈余合意性(Hu,2019)提出了合作博弈解新的公理,即联盟缺额合意性,并证明了除了不超过2个局中人合作博弈的平凡情形之外,联盟缺额合意性与合作博弈解的有效性互斥.其次,通过对联盟缺额进行平均化引入了平均联盟缺额合意性,进一步结合有效性和可加性实现了均分不可分贡献值的公理化刻画.最后,将相关公理化结果拓展到了权重均分不可分贡献值(Hou等,2019).

In this paper,we firstly provide an axiom for solutions of TU games,called the coalitional gap desirability(CGD),by adapting the recent coalitional surplus desirability(Hu,2019).It is verified that no solution satisfies both the CGD and the classical efficiency except for the trivial situation where there are no more than two players in a cooperative game.We then introduce an adapted axiom by averaging coalitions’gap,namely the average coalitional gap desirability.The equal allocation of nonseparable contributions value(ENSC value)is axiomatized by this averaged version together with the efficiency and additivity axioms.Finally,the axiomatic results are extended to the weighted ENSC value(Hou,et al.,2019).