The equivalence of the minimal dominant set and the myopic stable set for coalition function form games

• 成果类型: Article
• 署名作者: Herings, P. Jean-Jacques; Koczy, Laszlo A.
• 署名单位: Maastricht University; HUN-REN; HUN-REN Centre for Economic & Regional Studies; Budapest University of Technology & Economics
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2021.02.003
• 发表日期: 2021
• 页码: 67-79
• 关键词: Coalition structure core; Sequential dominance

摘要

In cooperative games, the coalition structure core is, despite its potential emptiness, one of the most popular solutions. While it is a fundamentally static concept, the consideration of a sequential extension of the underlying dominance correspondence gave rise to a selection of non-empty generalizations. Among these, the payoff-equivalence minimal dominant set and the myopic stable set are defined by a similar set of conditions. We identify some problems with the payoff-equivalence minimal dominant set and propose an appropriate reformulation called the minimal dominant set. We show that replacing asymptotic external stability by sequential weak dominance leaves the myopic stable set unaffected. The myopic stable set is therefore equivalent to the minimal dominant set. (C) 2021 The Author(s). Published by Elsevier Inc.