Strong Duality for a Multiple-Good Monopolist
Constantinos Daskalakis, Alan Deckelbaum, Christos Tzamos
Econometrica · 2017 · Volume 85 · Issue 3
Abstract
We characterize optimal mechanisms for the multiple-good monopoly problem and provide a framework to find them. We show that a mechanism is optimal if and only if a measureμderived from the buyer's type distribution satisfies certain stochastic dominance conditions. This measure expresses the marginal change in the seller's revenue under marginal changes in the rent paid to subsets of buyer types. As a corollary, we characterize the optimality of grand-bundling mechanisms, strengthening several results in the literature, where only sufficient optimality conditions have been derived. As an application, we show that the optimal mechanism fornindependent uniform items each supported on [c,c+1] is a grand-bundling mechanism, as long ascis sufficiently large, extending Pavlov's result for two items Pavlov, 2011. At the same time, our characterization also implies that, for allcand for all sufficiently largen, the optimal mechanism fornindependent uniform items supported on [c,c+1]is nota grand-bundling mechanism.
Keywords
Revenue maximization, mechanism design, strong duality, grand bundling
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