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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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  • Martín Egozcue

    ()
    (Universidad de la República - Facultad de Ciencias Sociales)

  • Sébastien Massoni

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne)

  • Wing-Keung Wong

    ()
    (Hong Kong Baptist University - Department of Economics and the Institute for Computational Mathematics)

  • Ričardas Zitikis

    ()
    (Department of Statistical and Actuarial Sciences - University of Western Ontario)

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.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00747008.

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Date of creation: Sep 2012
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Handle: RePEc:hal:cesptp:halshs-00747008

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Related research

Keywords: Bundling; marketing; mental accounting; portfolio theory; value fonction; utility function; majorization; functional inequalities; Bell number.;

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  1. Richard Thaler, 1985. "Mental Accounting and Consumer Choice," Marketing Science, INFORMS, vol. 4(3), pages 199-214.
  2. Egozcue, Martín & García, Luis Fuentes & Wong, Wing-Keung & Zitikis, Ricardas, 2011. "Do investors like to diversify? A study of Markowitz preferences," European Journal of Operational Research, Elsevier, vol. 215(1), pages 188-193, November.
  3. Tversky, Amos & Kahneman, Daniel, 1992. " Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
  4. Fishburn, Peter C. & Duncan Luce, R., 1995. "Joint receipt and Thaler's hedonic editing rule," Mathematical Social Sciences, Elsevier, vol. 29(1), pages 33-76, February.
  5. Heath, Timothy B & Chatterjee, Subimal & France, Karen Russo, 1995. " Mental Accounting and Changes in Price: The Frame Dependence of Reference Dependence," Journal of Consumer Research, University of Chicago Press, vol. 22(1), pages 90-97, June.
  6. Kobberling, Veronika & Wakker, Peter P., 2005. "An index of loss aversion," Journal of Economic Theory, Elsevier, vol. 122(1), pages 119-131, May.
  7. Alexander Ljungqvist & William J. Wilhelm, 2005. "Does Prospect Theory Explain IPO Market Behavior?," Journal of Finance, American Finance Association, vol. 60(4), pages 1759-1790, 08.
  8. Sonya Seongyeon Lim, 2006. "Do Investors Integrate Losses and Segregate Gains? Mental Accounting and Investor Trading Decisions," The Journal of Business, University of Chicago Press, vol. 79(5), pages 2539-2574, September.
  9. 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.
  10. al-Nowaihi, Ali & Bradley, Ian & Dhami, Sanjit, 2008. "A note on the utility function under prospect theory," Economics Letters, Elsevier, vol. 99(2), pages 337-339, May.
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