Fair stable sets of simple games

• 成果类型: Article
• 署名作者: Talamas, Eduard
• 署名单位: Harvard University
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2017.08.004
• 发表日期: 2018
• 页码: 574-584
• 关键词: Fair stable set; Simple game; Compound simple game; symmetry; aggregation

摘要

Simple games are abstract representations of voting systems and other group-decision procedures. A stable set-or von Neumann-Morgenstern solution-o f a simple game represents a standard of behavior that satisfies certain internal and external stability properties. Compound simple games are built out of component games, which are, in turn, players of a quotient game. I describe a method to construct fair or symmetry-preserving stable sets of compound simple games from fair stable sets of their quotient and components. This method is closely related to the composition theorem of Shapley (1963c), and contributes to the answer of a question that he formulated: What is the set g of simple games that admit a fair stable set? In particular, this method shows that the set g includes all simple games whose factors or quotients in their unique factorization of Shapley (1967) are in g, and suggests a path to characterize g. (C) 2017 Elsevier Inc. All rights reserved.