Optimal Bundling Strategies for Complements and Substitutes under Heavy-Tailed Dependent Valuations

We develop a general framework for modelling the optimal bundling strategies of a multiprod- uct monopolist providing goods that have extreme and dependent valuations by consumers. We show that the optimal bundling strategies crucially depend on the degree of heavy-tailedness of consumers’ valuations and preferences for the goods, their dependence structure, and the degrees of complementarity and substitutability among the goods provided. For substitutes with suffi- ciently high degree of substitutability as compared to the degree of heavy-tailedness of consumers’ valuations, the seller’s optimal strategy is to provide goods separately. On the other hand, pro- vision of the goods as a single bundle is optimal for the seller in the case of complements and substitutes with relatively low degree of substitutability. The conclusions hold regardless of the marginal costs of producing the goods. They further hold for a wide class of dependent valuations with possibly heavy-tailed shocks affecting all preferences and valuations of the consumers. We discuss how these results may help to explain several bundling strategies commonly observed in real-world markets.

Link to work
working papers