Integration-segregation decisions under general value functions: "Create your own bundle -- choose 1, 2, or all 3 !"

Martín Egozcue (megozcue@correo.um.edu.uy), Sébastien Massoni, Wing-Keung Wong and Ričardas Zitikis (zitikis@stats.uwo.ca)
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Martín Egozcue: UDELAR - Universidad de la República [Montevideo]
Ričardas Zitikis: Department of Statistical and Actuarial Sciences - UWO - University of Western Ontario

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Abstract: Whether to keep products segregated (e.g., unbundled) or integrate some or all of them (e.g., bundle) has been a problem of profound interest in areas such as portfolio theory in finance, risk capital allocations in insurance, and marketing of consumer products. Such decisions are inherently complex and depend on factors such as the underlying product values and consumer preferences, the latter being frequently described using value functions, also known as utility functions in economics. In this paper, we develop decision rules for multiple products, which we generally call 'exposure units' to naturally cover manifold scenarios spanning well beyond 'products'. Our findings show, for example, that the celebrated Thaler's principles of mental accounting hold as originally postulated when the values of all exposure units are positive (i.e., all are gains) or all negative (i.e., all are losses). In the case of exposure units mixed-sign values, decision rules are much more complex and rely on cataloging the Bell-number of cases that grow very fast depending on the number of exposure units. Consequently, in the present paper we provide detailed rules for the integration and segregation decisions in the case up to three exposure units, and partial rules for the arbitrary number of units.

Keywords: Bell number; Bundling; marketing; mental accounting; portfolio theory; value fonction; utility function; majorization; functional inequalities; Bell number.; Package; comptabilité mentale; théorie de portefeuille; fonctions d'utilité; majorisation; inégalités fonctionnelles; nombre de Bell. (search for similar items in EconPapers)
Date: 2012-09
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00747008v1
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Citations: View citations in EconPapers (3)

Published in 2012

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Working Paper: Integration-segregation decisions under general value functions: "Create your own bundle -- choose 1, 2, or all 3 !" (2012)
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