eparately Convex and Separately Continuous Preferences: On Results of Schmeidler, Shafer and Bergstrom-Parks-Rader

Aniruddha Ghosh (), M. Ali Khan () and Metin Uyanik ()
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Aniruddha Ghosh: Department of Economics, Cal Poly University
M. Ali Khan: Department of Economics, Johns Hopkins University
Metin Uyanik: School of Economics, University of Queensland

No 2502, Working Papers from California Polytechnic State University, Department of Economics

Abstract: We provide necessary and sufficient conditions for a correspondence taking values in a finite-dimensional Euclidean space to be open so as to revisit the pioneering work of Schmeidler(1969), Shafer (1974), Shafer-Sonnenschein (1975) and Bergstrom-Rader-Parks (1976) to answer several questions they and their followers left open. We introduce the notion of separate convexity for a correspondence and use it to relate to classical notions of continuity while giving salience to the notion of separateness in the interplay of separate continuity and separate convexity of binary relations. As such, we provide a consolidation of the convexity-continuity postulates from a broad inter-disciplinary perspective and comment on how the qualified notions proposed here have implications of substantive interest for choice theory.

Keywords: Separately convex; separately continuous; linearly continuous; graph-continuous; section-continuous; preferences; correspondences (search for similar items in EconPapers)
JEL-codes: C00 C02 D01 D11 D51 D81 (search for similar items in EconPapers)
Pages: 23 pages
Date: 2025
New Economics Papers: this item is included in nep-dcm and nep-mic
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