Optimal Bundling Strategies for Complements and Substitutes with Heavy-Tailed Valuations

Abstract

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 long-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 not extremely 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 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 long-tailed tastes.

Keywords: Optimal bundling strategies, multiproduct monopolist, Vickrey auction, substitutes, complements, heavy-tailed valuations, tastes, robustness

JEL Classification: D42, D44, L12, L21