🤖 AI Summary
This study addresses the design of optimal bundling mechanisms for complementary goods in multidimensional type spaces. To tackle the pricing and allocation challenges arising from complementarities, the authors develop a multidimensional screening framework grounded in duality theory and employ geometric methods to characterize combinatorial preferences, recasting mechanism optimality as a coverage problem over “essential directions.” The key innovation is a “core–periphery” menu structure, governed by two critical thresholds: when a buyer’s valuation exceeds the lower threshold, the full bundle must be offered; above the higher threshold, the optimal mechanism consists of a fixed core bundle augmented with optional add-ons that cannot be sold separately. An “inclusivity” condition ensures the higher threshold remains finite, preventing exclusion of high-valuation buyers and thereby guaranteeing both completeness and optimality of the mechanism.
📝 Abstract
I develop a duality-based multi-dimensional screening framework with a geometric characterization of combinatorial preferences. For a mechanism to be optimal, the type distribution pins down \emph{required} directions of binding feasibility constraints, while the complementarity among bundles determines the \emph{covered} directions; optimality reduces to full coverage of required directions. I apply the framework to a one-parameter family in which every bundle containing a fixed \emph{core} of items earns a complementarity premium. Two thresholds organize the optimum: above a lower threshold the grand bundle must be offered; above a higher threshold a \emph{core-peripheral} menu -- a bundled core with optional add-ons that are not sold standalone -- is optimal. The tight distributional condition for finiteness of the higher threshold is \emph{inclusivity}, that the menu exclude no near-top buyer.