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The Intermediate Value Theorem and Decision-Making in Psychology and Economics: An Expositional Consolidation

Author

Listed:
  • Aniruddha Ghosh

    (Department of Economics, Johns Hopkins University, Baltimore, MD 21218, USA)

  • Mohammed Ali Khan

    (Department of Economics, Johns Hopkins University, Baltimore, MD 21218, USA)

  • Metin Uyanik

    (School of Economics, University of Queensland, Brisbane, QLD 4072, Australia)

Abstract

On taking the intermediate value theorem (IVT) and its converse as a point of departure, this paper connects the intermediate value property (IVP) to the continuity postulate typically assumed in mathematical economics, and to the solvability axiom typically assumed in mathematical psychology. This connection takes the form of four portmanteau theorems, two for functions and the other two for binary relations, that give a synthetic and novel overview of the subject. In supplementation, the paper also surveys the antecedent literature both on the IVT itself, as well as its applications in economic and decision theory. The work underscores how a humble theorem, when viewed in a broad historical frame, bears the weight of many far-reaching consequences; and testifies to a point of view that the apparently complicated can sometimes be under-girded by a most basic and simple execution.

Suggested Citation

  • Aniruddha Ghosh & Mohammed Ali Khan & Metin Uyanik, 2022. "The Intermediate Value Theorem and Decision-Making in Psychology and Economics: An Expositional Consolidation," Games, MDPI, vol. 13(4), pages 1-24, July.
    • Handle: RePEc:gam:jgames:v:13:y:2022:i:4:p:51-:d:863546
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    References listed on IDEAS

    as
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    Cited by:

    1. Metin Uyanik & Aniruddha Ghosh & M. Ali Khan, 2023. "Separately Convex and Separately Continuous Preferences: On Results of Schmeidler, Shafer, and Bergstrom-Parks-Rader," Papers 2310.00531, arXiv.org.

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