运筹学学报

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图限制下合作对策的t值

王文文, 孙浩, 韩卫彬   

  1. 西北工业大学
  • 收稿日期:2011-01-26 修回日期:2011-09-07 出版日期:2011-12-15 发布日期:2011-12-19
  • 通讯作者: 王文文 E-mail:wangwenwen0506@126.com

The $\tau$-value of Cooperative Games Restricted by Graph

 WANG  Wen-Wen, SUN  Hao, HAN  Wei-Bin   

  • Received:2011-01-26 Revised:2011-09-07 Online:2011-12-15 Published:2011-12-19

摘要: 本文给出图限制下合作对策 值的结构,这个单值解可看作是由Tijs提出的经典合作对策 值的推广.当合作图为完全图时,准均衡图对策的 值与经典合作对策下的准均衡对策的 值一致. 值是基于核心的上界和对应于上界的超量得到对策的一个妥协解.利用分支有效性,S-均衡下的相对不变性和限制成比例性讨论了 值的公理化方法.最后一部分讨论两类特殊图对策的 值.

关键词: 图对策, $\tau$值, 准均衡, 分支有效

Abstract: We first study the  $\tau$-value for graph-restricted games and provide its explicit construction.
The one-point solution could be considered as a natural extension of the  $\tau$-value introduced by
Tijs for classical cooperative games. When the cooperation graph is complete, the  $\tau$-value for
graph-restricted games coincides with the  $\tau$-value for classical cooperative games. Then we
provide an axiomatization of the  $\tau$-value for graph-restricted games via component efficiency,
 relative invariance under S-equivalence and restricted proportionality. The last section introduces
 the  $\tau$-value for two special classes of graph-restricted games.

Key words: graph-restricted games, $\tau$-value, quasibalanced, component efficiency