Hierarchies of ambiguous beliefs

• 成果类型: Article
• 署名作者: Ahn, David S.
• 署名单位: University of California System; University of California Berkeley
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2006.08.004
• 发表日期: 2007
• 页码: 286-301
• 关键词: Ambiguity; Knightian uncertainty; Bayesian games; universal type space

摘要

We present a theory of interactive beliefs analogous to Mertens and Zamir [Formulation of Bayesian analysis for games with incomplete information, Int. J. Game Theory 14 (1985) 1-29] and Brandenburger and Dekel [Hierarchies of beliefs and common knowledge, J. Econ. Theory 59 (1993) 189-198] that allows for hierarchies of ambiguity. Each agent is allowed a compact set of beliefs at each level, rather than just a single belief as in the standard model. We propose appropriate definitions of coherency and common knowledge for our types. Common knowledge of coherency closes the model, in the sense that each type homeomorphically encodes a compact set of beliefs over the others' types. This space universally embeds every implicit type space of ambiguous beliefs in a beliefs-preserving manner. An extension to ambiguous conditional probability systems [P. Battigalli, M. Siniscalchi, Hierarchies of conditional beliefs and interactive epistemology in dynamic games, J. Econ. Theory 88 (1999) 188-230] is presented. The standard universal type space and the universal space of compact continuous possibility structures are epistermically identified as subsets. (C) 2006 Elsevier Inc. All rights reserved.