Formalizing common belief with no underlying assumption on individual beliefs

• 成果类型: Article
• 署名作者: Fukuda, Satoshi
• 署名单位: Bocconi University; Bocconi University
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2020.02.007
• 发表日期: 2020
• 页码: 169-189
• 关键词: Common belief; common knowledge; Logical omniscience; Non-monotonic reasoning; Common bases; Strict dominance

摘要

This paper formalizes common belief among players with no underlying assumption on their individual beliefs. Especially, players may not be logically omniscient, i.e., they may not believe logical consequences of their beliefs. The key idea is to use a novel concept of a common basis: it is an event such that, whenever it is true, every player believes its logical consequences. The common belief in an event obtains when a common basis implies the mutual belief in that event. If players' beliefs are assumed to be true, then common belief reduces to common knowledge. The formalization nests previous axiomatizations of common belief and common knowledge which have assumed players' logical monotonic reasoning. Under this formalization, unlike others, if players have common belief in rationality then their actions survive iterated elimination of strictly dominated actions even if their beliefs are not monotonic. (C) 2020 The Author(s). Published by Elsevier Inc.