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.

This paper estimates an equilibrium model of stock price behaviour in which changes in exponentially de-trended dividends and prices are normally distributed and exogenous “noise traders” interact with “smart-money” investors who have constant absolute risk aversion. The model can explain the volatility and predictability of U.S. stock returns in the period 1871–1986 using either a low discount rate (4% or below) and a large constant risk discount on the stock price, or a higher discount rate (5% or above) and noise trading correlated with fundamentals. The data are not well able to distinguish between these explanations.

We describe a symmetric continuous-time model of trading among relatively overconfident, oligopolistic informed traders with exponential utility. Traders agree to disagree about the precisions of their continuous flows of Gaussian private information. The price depends on a trader’s inventory (permanent price impact) and the derivative of a trader’s inventory (temporary price impact). More disagreement makes the market more liquid; without enough disagreement, there is no trade. Target inventories mean-revert at the same rate as private signals. Actual inventories smoothly adjust towards target inventories at an endogenous rate which increases with disagreement. Faster-than-equilibrium trading generates “flash crashes” by increasing temporary price impact. A “Keynesian beauty contest” dampens price fluctuations.