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Title: Majorization theory, heavy-tailedness and robustness in economics, finance, econometrics and engineering Authors:  Rustam Ibragimov - Imperial College London and St. Petersburg State University (United Kingdom) [presenting]
Artem Prokhorov - University of Sydney (Australia)
Johan Walden - UC Berkeley, Haas School of Business (United States)
Abstract: Using majorization theory and extending earlier works in the field, we develop a framework that allows one to model the optimal bundling problem of a multiproduct monopolist providing interrelated goods with an arbitrary degree of complementarity or substitutability. Characterizations of optimal bundling strategies are derived for the seller in the case of heavy-tailed valuations and tastes for the products. We show, in particular, that if goods provided in a Vickrey auction or any other revenue equivalent auction are substitutes and bidders' tastes for the objects are moderately heavy-tailed, then the monopolist prefers separate provision of the products. However, if the goods are complements and consumers' tastes are extremely thick-tailed, then the seller prefers providing the products on a single auction. We also present results on consumers' preferences over bundled auctions for complements and substituties in the case when their valuations exhibit heavy-tailedness. In addition, we obtain characterizations of optimal bundling strategies for a monopolist who provides complements or substitutes for profit-maximizing prices to buyers with heavy-tailed tastes.