Advances in Mechanism and Information Design
Paper Session
Friday, Jan. 3, 2025 2:30 PM - 4:30 PM (PST)
- Chair: Kai Hao Yang, Yale University
Nested Bundling
Abstract
A nested bundling strategy creates menus in which more expensive bundles includeall the goods of the less expensive ones. We study when nested bundling is optimal
and determine which nested menu is optimal, when consumers differ in one dimension. We introduce a partial order on the set of bundles, defined by (i) set inclusion
and (ii) sales quantity when sold alone. We show that, under quasiconcavity assumptions, if the undominated bundles with respect to this partial order are nested, then
nested bundling is optimal. We provide an iterative procedure to determine the minimal optimal menu that consists of a subset of the undominated bundles. The proof
technique involves a new constructive monotone comparative statics theorem. We
present partial converses. Additionally, we provide distributionally robust characterizations of nested bundling. We also show that under suitable conditions it is possible
to extend our analysis to allow multidimensional heterogeneity.
Improvable Equilibria
Abstract
In many settings, agents can communicate---either directly or through intermediaries---before they engage in strategic interactions. We explore when such communication can be beneficial in general strategic contexts. We show that this question reduces, for any non-degenerate objective, to determining when Nash equilibria are extreme points within the set of correlated equilibria. Our results demonstrate that any sufficiently random mixed Nash equilibrium, involving at least three agents randomizing, can always be improved by either correlating agents' actions or switching to a less random equilibrium, regardless of the underlying objective. As a result, symmetric equilibria in a variety of symmetric environments---such as auctions, voting, and matching---are inherently suboptimal, no matter the goal.Non-Discriminatory Personalized Pricing
Abstract
A unit mass of consumers with unit demands purchase a product from a monopolist. Consumers have a binary protected characteristic, which is associated with value distributions ranked in the likelihood ratio order. We characterize the revenue-maximizing market segmentation and pricing strategy subject to a non-discriminatory constraint, where consumers with different protected characteristics must face the same prices. This problem is equivalent to an optimal transport with a non-supermodular objective function. Outcomes induced by revenue-maximizing segmentations only differ in the surplus of consumers with the characteristic associated with low values, with the lowest surplus level being zero. In the meantime, consumers with the characteristic associated with high values always retain positive surplus, but suffer from deadweight losses.JEL Classifications
- D8 - Information, Knowledge, and Uncertainty
- D4 - Market Structure, Pricing, and Design