The strategic choice of spatial price policy in duopoly depends on the rules of price competition. When one firm leads and the other follows, spatial price discrimination is the best strategy. If roles are reversed, pricing depends on consumer reservation value. For low values, both firms either price uniformly or discriminate. For medium values, discrimination is best but leads to a dilemma. With high values, one firm prices uniformly while the other discriminates. Simultaneous price competition results in a mixed strategies equilibrium, with firms either pricing uniformly or discriminating.