Non-existence of continuous choice functions

• 成果类型: Article
• 署名作者: Nishimura, Hiroki; Ok, Efe A.
• 署名单位: New York University
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2014.07.006
• 发表日期: 2014
• 页码: 376-391
• 关键词: Choice functions; rationality; continuity

摘要

Let X be a compact, or path-connected, metric space whose topological dimension is at least 2. We show that there does not exist a continuous choice function (i.e., single-valued choice correspondence) defined on the collection of all finite feasible sets in X. Not to be void of content, therefore, a revealed preference theory in the context of most infinite consumption spaces must either relinquish the fundamental continuity property or allow for multi-valued choice correspondences. (C) 2014 Published by Elsevier Inc.