Market segregation in the presence of customer discrimination

I consider a market with two firms, a minority group of customers, and a bigoted (racist, ethnocentric, xenophobic, or sexist) majority group of customers. There exists a Nash equilibrium with full segregation in which a low-price firm serves only the minority and a high-price firm serves only the majority. There is also a partial-integration equilibrium in which a high-price firm serves only the majority while a low-price firm serves both the minority and majority. Paradoxically, if the minority group is sufficiently big and the majority is sufficiently prejudiced, then both equilibria hold in the sense that the high-price firm does not lose customers, although its competitor charges a lower price. If the firms can price discriminate, none of these equilibria will hold. The partial integration equilibrium depends on how the prejudice of the majority is modelled.