Belief consistency and trade consistency

• 成果类型: Article
• 署名作者: Lehrer, Ehud; Samet, Dov
• 署名单位: Tel Aviv University; INSEAD Business School; Tel Aviv University
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2013.11.005
• 发表日期: 2014
• 页码: 165-177
• 关键词: Type spaces; common prior; No-trade theorems; Agreeing to disagree; Belief consistency; Dutch books

摘要

Interpersonal consistency can be described in epistemic terms as a property of beliefs, or in economic terms as the impossibility of certain trades. The existence of a common prior from which all agents' beliefs are derived is of the first kind. The non-existence of an agreeable bet, that is, a contingent zero-sum trade which is always favorable to all agents, is of the second kind. It is well established that these two notions of consistency are equivalent for finite type spaces but not for countable ones. We present three equivalences of epistemic consistency and economic consistency conditions for countable type spaces, defining in this way three levels of consistency of type spaces: weak consistency, consistency, and strong consistency. These three levels coincide in the finite case. We fully analyze the level of consistency of type spaces based on the knowledge structure of Rubinstein's email game. The new notion of belief consistency introduced here helps to justify the requirement of boundedness of payoff functions in countable type spaces by showing that in a large class of spaces there exists an agreeable unbounded bet even when a common prior exists. (C) 2013 Elsevier Inc. All rights reserved.