Revenue maximization in combinatorial auctions (and other multidimensional selling settings) is one of the most important and most elusive problems in mechanism design. The design problem is NP-complete, and the optimal designs include features that are not acceptable in many applications, such as favoring some bidders over others and randomization. In this paper, we instead study a common revenue-enhancement approach - bundling - in the context of the most commonly studied combinatorial auction mechanism, the Vickrey-Clarke-Groves (VCG) mechanism. A second challenge in mechanism design for combinatorial auctions is that the prior distribution on each bidder’s valuation can be doubly exponential. Such priors do not exist in most applications. Rather, in many applications (such as premium display advertising markets), there is essentially a point prior, which may not be accurate. We adopt the point prior model, and prove robustness to inaccuracy in the prior. Then, we present a branch-and-bound framework for finding the optimal bundling. We introduce several techniques for branching, upper bounding, lower bounding, and lazy bounding. Experiments on CATS distributions validate the approach and show that our techniques dramatically improve scalability over a leading general-purpose MIP solver.

40 pages

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