Limits on price discrimination when market values are unknown
The Limits of Price Discrimination When the Market Is Unknown
Computer Science and Game Theory
Summary
This work studies how sellers can charge different prices to different groups of buyers when they do not know exactly how much buyers value a product. The authors find that even with some market segmentation, the possible trade-offs between how much profit sellers make and how much value buyers get form a clear, predictable shape. Sometimes, sellers don’t need to segment the market to reach the best outcomes, and splitting the market into two extreme groups is enough to maximize efficiency in other cases. They also find mathematical bounds on consumer surplus given a fixed seller profit when values vary continuously.
What this means in practice
- •For pricing strategists: Use theoretical limits to design pricing schemes when customer value distributions are not fully known, guiding segmentation strategies under profit constraints.
- •For economic modelers: Incorporate the convex trade-off between consumer and producer surplus into models where exact buyer valuations are unknown, improving market predictions.
A theory result. No direct application yet.
Authors
Irfan Tekdir
Abstract
Bergemann, Brooks, and Morris (2015) characterize the consumer and producer surplus pairs that segmentation can produce when the distribution of values is known. I fix only the set of possible values and characterize the pairs that some market and some segmentation can produce. They form a convex polygon. Its outer edge is the largest efficient surplus a market can have when its uniform-price profit is capped, net of that profit, and truncated equal-revenue markets attain it. At the values no segmentation is needed; strictly between two values, reaching the frontier requires splitting a market into two extremal markets. With a continuum of values up to $\bar{v}$, consumer surplus is at most $π\ln(\bar{v}/π)$ when producer surplus (the seller's profit) is $π$, this bound is reached without segmentation, and no market gives consumers more than $\bar{v}/e$.