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运筹学学报

• 运筹学 •    下一篇

二元稳定网络的算法及模型

甄孟可1  高红伟1,2,* 刘树清1  纪海强1   

  1. 1. 青岛大学数学与统计学院, 山东青岛 266071 2. 山东省应用数学研究所, 山东青岛 266071
  • 收稿日期:2016-02-01 出版日期:2016-09-15 发布日期:2016-09-15
  • 通讯作者: 高红伟 gaohongwei@qdu.edu.cn
  • 基金资助:

    国家自然科学基金(Nos. 71571108, 71171120), 国家自然科学基金国际(地区) 合作交流项目(No. 71411130215), 国家自然科学基金国际(地区)合作研究项目(No. 61661136002), 教育部高等学校博士学科点专项科研基金(No. 20133706110002), 山东省自然科学基金(No. ZR2015GZ007), 青岛大学研究生教育创新计划项目(Nos. QDY12017, QDY13004)

The algorithm and model of pairwise stable networks

ZHEN Mengke1 GAO Hongwei1,2,*  LIU Shuqing1  JI Haiqiang1   

  1. 1. School of Mathematics and Statistics, Qingdao University, Qingdao 266071, Shandong, China 2. Institute of Applied Mathematics of Shandong, Qingdao 266071, Shandong, China
  • Received:2016-02-01 Online:2016-09-15 Published:2016-09-15

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摘要：

通过建立JW(Jackson-Wolinsky)规则之下二元稳定网络的等价条件, 给出其完整算法. 引入边支付后, 证明了增连接情形具有边支付的二元稳定网络集合是二元稳定网络集合与具有边支付的二元稳定网络集合的交集. 考察两个特定的网络模型, 系统分析了它们的二元稳定性.

关键词: 网络博弈, JW规则, 二元稳定性, 边支付

Abstract:

Firstly, by establishing equivalent condition of pairwise stability networks with Jackson-Wolinsky rules, this paper gives an complete algorithm to find pairwise stability network. Secondly, after the introduction of side payments, this paper proofs that the set of pairwise stability network allowing for side payments when adding links is the intersection of the set of pairwise stability network and the set of pairwise stability network allowing for side payments when adding and deleting links. Finally, two explicit pairwise stability network models are considered. Using the algorithm of pairwise stability networks, this paper systematically analyzes this two models’ pairwise stability.

Key words: network game, Jackson-Wolinsky rules, pairwise stability, side payments