A Simple and Approximately Optimal Mechanism for a Buyer with Complements

Abstract

Recent literature on approximately optimal revenue maximization has shown that in settings where agent valuations for items are complement free, the better of selling the items separately and bundling them together guarantees a constant fraction of the optimal revenue. However, most real-world settings involve some degree of complementarity among items. The role that complementarity plays in the trade-off of simplicity versus optimality has been an obvious missing piece of the puzzle. In “A Simple and Approximately Optimal Mechanism for a Buyer with Complements,” the authors show that the same simple selling mechanism—the better of selling separately and as a grand bundle—guarantees a $\Theta(d)$ fraction of the optimal revenue, where $d$ is a measure of the degree of complementarity. One key modeling contribution is a tractable notion of “degree of complementarity” that admits meaningful results and insights—they demonstrate that previous definitions fall short in this regard.