On core stability, vital coalitions, and extendability

• 成果类型: Article
• 署名作者: Shellshear, Evan; Sudholter, Peter
• 署名单位: University of Southern Denmark; University of Bielefeld
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2009.01.005
• 发表日期: 2009
• 页码: 633-644
• 关键词: TU game; core; stable set; Extendability; Vital coalition

摘要

If a TU game is extendable, then its core is a stable set. However, there are many TU games with a stable core that are not extendable. A coalition is vital if there exists some core element x such that none of the proper subcoalitions is effective for x. It is exact if it is effective for some core element. If all coalitions that are vital and exact are extendable, then the game has a stable core. It is shown that the contrary is also valid for matching games, for simple flow games, and for minimum coloring games. (C) 2009 Elsevier Inc. All rights reserved.