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

Aniruddha Ghosh, M. Khan and Metin Uyanık
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Aniruddha Ghosh: Department of Economics, Johns Hopkins University, Baltimore, MD 21218, USA

Games, 2022, vol. 13, issue 4, 1-24

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.

Keywords: intermediate value theorem; intermediate value property; solvability; continuity; wold-continuity; archimedeanity; decision theory; measurement theory (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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