Non-existence of continuous choice functions

Hiroki Nishimura, Efe A. Ok

    Research output: Contribution to journalArticlepeer-review

    Abstract

    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.

    Original languageEnglish (US)
    Pages (from-to)376-391
    Number of pages16
    JournalJournal of Economic Theory
    Volume153
    Issue number1
    DOIs
    StatePublished - Sep 2014

    Keywords

    • Choice functions
    • Continuity
    • Rationality

    ASJC Scopus subject areas

    • Economics and Econometrics

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