A note on equivalence of consistency and bilateral consistency through converse consistency

• 成果类型: Article
• 署名作者: Driessen, Theo; Hu, Cheng-Cheng
• 署名单位: University of Twente; Southern Taiwan University of Science & Technology
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2008.01.011
• 发表日期: 2009
• 页码: 644-648
• 关键词: Coalitional TU-game; Reduced game; (Bilateral) Consistency; Converse consistency

摘要

In the framework of (set-valued or single-valued) solutions for coalitional games with transferable utility, the three notions of consistency, bilateral consistency, and converse consistency are frequently used to provide axiomatic characterizations of a particular solution (like the core, prekernel, prenucleolus, Shapley value). Our main equivalence theorem claims that a solution satisfies consistency (with respect to an arbitrary reduced game) if and only if the solution satisfies both bilateral consistency and converse consistency (with respect to the same reduced game). The equivalence theorem presumes transitivity of the reduced game technique as well as difference independence on payoff vectors for two-person reduced games. (C) 2008 Published by Elsevier Inc.