A Tale of Two Monopolies

2025-06-07

AI Summary

This paper studies revenue-maximizing mechanism design for a multi-product monopolist. We develop an extended Bulow–Roberts marginal analysis framework—the first systematic application of such methodology to general multidimensional type distributions and arbitrary value structures (additive, complementary, or substitutable)—to rigorously characterize the marginal effect of bundle price perturbations on total revenue. For the symmetric two-dimensional case, we fully characterize the optimal mechanism, derive universal first-order optimality conditions, and explicitly distinguish pricing criteria for bundles with positive versus zero demand. Moreover, we identify necessary conditions for randomized pricing. Under mild regularity assumptions, our analysis achieves a theoretical breakthrough, substantially advancing the frontier of optimal multi-product pricing.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

We apply marginal analysis `a la Bulow and Roberts (1989) to characterize the revenue-maximizing selling mechanism for a multiproduct monopoly. Specifically, we derive the revenue change due to a price perturbation on any subset of bundles holding the prices of other bundles fixed. In an optimal mechanism, total revenue must not increase with any small price change for bundles with positive demand, nor with a small price decrease for bundles with zero demand. For any symmetric two-dimensional type distribution satisfying mild regularity conditions, the marginal analysis fully characterizes the optimal mechanism, whether the buyer's valuations are additive or exhibit complementarity or substitutability. For general type distributions, the analysis identifies which bundles must carry positive or zero demand and provides conditions under which randomization is necessary.

Problem

• Characterize revenue-maximizing mechanism for multiproduct monopoly
• Analyze price impact on bundles under additive or complementary valuations
• Determine optimal bundle demand and randomization conditions

Innovation

• Marginal analysis for multiproduct monopoly mechanism
• Revenue change via price perturbation on bundles
• Characterizes optimal mechanism for type distributions