Optimal Bundling Strategies in Multiobject Auctions of Complements or Substitutes

We consider a problem at the interface of auctions and bundling. Our revenue-maximizing seller seeking to auction one unit each of two complements or substitutes in the best-of-three formats: the auction of the bundle, separate auctions of the individual items, and a combinatorial auction. We draw on an analytical model to address the following questions: (i) Which of the auctioning strategies is optimal under the second-price, sealed-bid format? (ii) What is the optimal strategy for the bidders? (iii) When the objects are asymmetrically valued (e.g., Super Bowl ticket versus souvenir), what is the optimal auctioning sequence under the pure components strategy? Our results suggest that separate auctions of the two objects are superior to the auction of the bundle for most substitutes and even moderate complements when there are at least four bidders. The auction of the pure bundle is better suited for strong complements or with too few bidders. When the combinatorial auction is an available option, it weakly dominates the auction of the pure bundle but has domains of inferiority relative to the separate auctions. When the objects are asymmetric in value, it is optimal to auction the higher-valued object first.