We consider a market that may be segmented and is served by a single seller. The surplus of each consumer in a segment depends on the price that the seller optimally charges, and this optimal price depends on the set of consumers in that segment. This gives rise to a novel cooperative game between consumers that determines market segmentation.  We study several solution concepts.  The most demanding solution concept, the core, requires that there is no objection to the segmentation by a coalition of consumers who benefit by forming a new segment. We show that the core is empty except for trivial cases.  We then introduce a new solution concept, stability.  A segmentation is stable if for each possible objection by a coalition, there is a counter-objection by a coalition in the original segmentation. We characterize stable segmentations as ones that are efficient and ``saturated,'' which means that the segments are maximal in some sense.  We use this characterization to constructively show that stable segmentations 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. Our weakest solution concept, fragmentation-proofness, rules out objections by coalitions that include consumers from more than one segment. We show that a segmentation is fragmentation-proof if and only if it is efficient.