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

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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

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  • Martín Egozcue & Sébastien Massoni & Wing-Keung Wong & Ri?ardas Zitikis, 2012. "Integration-segregation decisions under general value functions: "Create your own bundle — choose 1, 2, or all 3!"," Documents de travail du Centre d'Economie de la Sorbonne 12057, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  • Handle: RePEc:mse:cesdoc:12057
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    1. Mohammed Abdellaoui & Han Bleichrodt & Olivier L’Haridon, 2008. "A tractable method to measure utility and loss aversion under prospect theory," Journal of Risk and Uncertainty, Springer, vol. 36(3), pages 245-266, June.
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    Keywords

    Bundling; marketing; mental accounting; portfolio theory; value function; utility function; majorization; functional inequalities; Bell number;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G02 - Financial Economics - - General - - - Behavioral Finance: Underlying Principles
    • M31 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Marketing and Advertising - - - Marketing

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