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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Aniruddha Ghosh & M. Ali Khan & Metin Uyanik, 2025. "eparately Convex and Separately Continuous Preferences: On Results of Schmeidler, Shafer and Bergstrom-Parks-Rader," Working Papers 2502, California Polytechnic State University, Department of Economics.
    • Handle: RePEc:cpl:wpaper:2502
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    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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