无圈超图对策上的有效平均树解

在超图对策中,平均树解(简称AT值)是一类重要的分支有效解.本文在大联盟能够形成的假设下,基于单而芳等(2017)和Béal等(2018)在无圈图对策上提出的有效平均树解,进一步提出了无圈超图对策上基于平均树解的一类有效解.该有效解先给每个参与者进行AT值分配,再将大联盟收益超出分支收益之和的剩余部分平均分配给每个参与者.首先,证明了该有效解可以由有效性、分支公平性和分支内盈余等分性这三个公理所唯一刻画.其次,通过算例分析了该有效解.通过与其他值比较发现,对处于关键位置的参与者,在该解下会获得更多的收益.

The efficient average tree solution for cycle-free hypergraph games

The average tree solution(for short,AT value)is an important component efficient solution for hypergraph games.Under the assumption that the grand coalition can be formed,based on the efficient average tree solution,we extend the efficient average tree solution(abbreviated by EAT value)proposed by Shan et al.(2017)and Beal et al.(2018)for cycle-free graph games to cycle-free hypergraph games.EAT value first assigns AT values to each player,and then the surplus of the worth of the grand coalition beyond the sum of the worth of all components is distributed equally to each player.Firstly,we show that EAT value can be characterized uniquely by three axioms:Efficiency,component fairness and equal distribution in the surplus within components.Also,we illustrate the EAT value by a numerical example and it is found that EAT value distributes more payoff to the players in key position.