Order on types based on monotone comparative statics

• 成果类型: Article
• 署名作者: Kunimoto, Takashi; Yamashita, Takuro
• 署名单位: Singapore Management University; Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2020.105082
• 发表日期: 2020
• 关键词: Common optimism; Least equilibrium; Greatest equilibrium; Interim correlated rationalizability; monotone comparative statics; supermodularity; universal type space

摘要

This paper introduces a novel concept of orders on types by which the so-called monotone comparative statics is valid in all supermodular games with incomplete information. We fully characterize this order in terms of what we call common optimism, providing a sense in which our order has a sharp epistemic interpretation. We say that type t(i)' is higher than type t(i) in the order of the common optimism if t(i)' is more optimistic about state than t(i) ; t(i)' is more optimistic that all players are more optimistic about state than t(i) ; and so on, ad infinitum. First, we show that whenever the common optimism holds, monotone comparative statics hold in all supermodular games. Second, we show the converse. We construct an optimism-elicitation game as a single supermodular game with the property that whenever the common optimism fails, monotone comparative statics fails as well. (C) 2020 Elsevier Inc. All rights reserved.