Competitive rational expectations models have the unsatisfactory property, dubbed the ``schizophrenia'' problem by Hellwig, that each trader takes the equilibrium price as given despite the fact that he influences that price. An examination of information aggregation in a non-competitive rational expectations model using a Nash equilibrium in demand functions shows that the schizophrenia problem is avoided by having each trader take into account the effect his demand has on the equilibrium price. Given a distribution of private information across traders, prices reveal less information than in the competition equilibrium, and prices no longer become fully informative in the limit as noise trading vanishes or as traders become risk neutral. With small traders, the model may become one of monopolistic competition, not perfect competition. In contrast to the competitive model, a reasonable model of endogenous acquisition of costly private information is obtained, even when traders are risk-neutral.