A Theory of Stable Market Segmentations

We consider a monopolistic seller in a market that may be segmented. The surplus of each consumer in a segment depends on the price that the seller optimally charges, which depends on the set of consumers in the segment. We study which segmentations may result from the interaction among consumers and the seller. Instead of studying the interaction as a non-cooperative game, we take a reduced-form approach and introduce a notion of stability that any resulting segmentation must satisfy. A stable segmentation is one that, for any alternative segmentation, contains a segment of consumers that prefers the original segmentation to the alternative one. Our main result characterizes stable segmentations as efficient and saturated. A segmentation is saturated if no consumers can be shifted from a segment with a high price to a segment with a low price without the seller optimally increasing the low price. We use this characterization to constructively show that stable segmentations always exist. Even though stable segmentations are efficient, they need not maximize average consumer surplus, and segmentations that maximize average consumer surplus need not be stable. Finally, we relate our notion of stability to solution concepts from cooperative game theory and show that stable segmentations satisfy many of them.