多选择NTU对策核心的一个非空条件及公理化

doi:10.15960/j.cnki.issn.1007-6093.2015.04.009

运筹学学报 ›› 2015, Vol. 19 ›› Issue (4): 97-106.doi: 10.15960/j.cnki.issn.1007-6093.2015.04.009

多选择NTU对策核心的一个非空条件及公理化

田海燕^1,*, 张刚²

1. 西北工业大学应用数学系, 西安 710072; 2. 河北师范大学数学与信息科学学院, 石家庄 050024

收稿日期:2015-02-06 出版日期:2015-12-15 发布日期:2015-12-15
通讯作者: 田海燕 tian\_math@163.com
基金资助:
河北省自然科学基金(No. A2014205152)

A non-empty condition and an axiomatization for the core of multi-choice NTU games

TIAN Haiyan^1,*, ZHANG Gang²

1.Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China; 2.College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, China

Received:2015-02-06 Online:2015-12-15 Published:2015-12-15

摘要/Abstract

摘要：

提出了\pi-均衡多选择NTU对策的概念,证明了\pi-均衡多选择NTU对策的核心非空, 定义了多选择NTU对策的非水平性质和缩减对策,给出了相容性和逆相容性等概念. 用个体合理性、单人合理性、相容性和逆相容性对非水平多选择NTU对策的核心进行了公理化.

关键词: 多选择NTU对策, 核心, \pi-均衡, 相容性

Abstract:

This paper introduces the concept of \pi-balanced multi-choice NTU games and proves that any \pi-balanced multi-choice NTU game has a non-empty core. The definitions of non-leveled multi-choice NTU games and reduced games are introduced and the concepts of consistency and converse consistency are also given. An axiomatization for the core of non-leveled multi-choice NTU games is provided by using individual rationality, one-person rationality, consistency and converse consistency.

Key words: multi-choice NTU games, cores, \pi-balancedness, consistency

田海燕, 张刚. 多选择NTU对策核心的一个非空条件及公理化[J]. 运筹学学报, 2015, 19(4): 97-106.

TIAN Haiyan, ZHANG Gang. A non-empty condition and an axiomatization for the core of multi-choice NTU games[J]. Operations Research Transactions, 2015, 19(4): 97-106.

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多选择NTU对策核心的一个非空条件及公理化

A non-empty condition and an axiomatization for the core of multi-choice NTU games

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