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Optimal Bundling Strategies Under Heavy-Tailed Valuations

Author

Listed:
  • Rustam Ibragimov

    (Department of Economics, Harvard University, Cambridge, Massachusetts 02138)

  • Johan Walden

    (Haas School of Business, University of California, Berkeley, Berkeley, California 94720)

Abstract

We develop a framework for the optimal bundling problem of a multiproduct monopolist, who provides goods to consumers with private valuations that are random draws from a distribution with heavy tails. We show that in the Vickrey auction setting, the buyers prefer separate provision of the goods to any bundles. We also provide a complete characterization of the optimal bundling strategies for a monopolist producer, who provides goods for profit-maximizing prices. For products with low marginal costs, the seller's optimal strategy is to provide goods separately when consumers' valuations are heavy-tailed and in a single bundle when valuations are thin-tailed. These conclusions are reversed for goods with high marginal costs. For simplicity, we use a specific class of independent and identically distributed random variables, but our results can be generalized to include dependence, skewness, and the case of nonidentical one-dimensional distributions.

Suggested Citation

  • Rustam Ibragimov & Johan Walden, 2010. "Optimal Bundling Strategies Under Heavy-Tailed Valuations," Management Science, INFORMS, vol. 56(11), pages 1963-1976, November.
  • Handle: RePEc:inm:ormnsc:v:56:y:2010:i:11:p:1963-1976
    DOI: 10.1287/mnsc.1100.1234
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    2. Chen, Zhimin & Ibragimov, Rustam, 2019. "One country, two systems? The heavy-tailedness of Chinese A- and H- share markets," Emerging Markets Review, Elsevier, vol. 38(C), pages 115-141.
    3. Banciu, M. & Ødegaard, F., 2016. "Optimal product bundling with dependent valuations: The price of independence," European Journal of Operational Research, Elsevier, vol. 255(2), pages 481-495.
    4. Liu Weihua & Yu Hui, 2017. "Pure Components VS Full Mixed Bundling When Stackelberg Pricing," Journal of Systems Science and Information, De Gruyter, vol. 5(5), pages 435-445, October.
    5. Gabaix, Xavier & Laibson, David & Li, Deyuan & Li, Hongyi & Resnick, Sidney & de Vries, Casper G., 2016. "The impact of competition on prices with numerous firms," Journal of Economic Theory, Elsevier, vol. 165(C), pages 1-24.
    6. Hemant K. Bhargava, 2013. "Mixed Bundling of Two Independently Valued Goods," Management Science, INFORMS, vol. 59(9), pages 2170-2185, September.
    7. Michael Grabchak, 2014. "Does value-at-risk encourage diversification when losses follow tempered stable or more general Lévy processes?," Annals of Finance, Springer, vol. 10(4), pages 553-568, November.
    8. Kevin M. Murphy & Ignacio Palacios-Huerta, 2016. "A Theory of Bundling Advertisements in Media Markets," NBER Working Papers 22994, National Bureau of Economic Research, Inc.
    9. Ibragimov, Rustam, 2014. "On the robustness of location estimators in models of firm growth under heavy-tailedness," Journal of Econometrics, Elsevier, vol. 181(1), pages 25-33.

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