We study trading behavior and the properties of prices in informationally complex markets. Our model is based on the single-period version of the linear-normal framework of [Kyle 1985]. We allow for essentially arbitrary correlations among the random variables involved in the model: the true value of the traded asset, the signals of strategic traders, the signals of competitive market makers, and the demand coming from liquidity traders. We first show that there always exists a unique linear equilibrium, characterize it analytically, and illustrate its properties in a series of examples. We then use this equilibrium characterization to study the informational efficiency of prices as the number of strategic traders becomes large. If the demand from liquidity traders is uncorrelated with the true value of the asset or is positively correlated with it (conditional on other signals), then prices in large markets aggregate all available information. If, however, the demand from liquidity traders is negatively correlated with the true value of the asset, then prices in large markets aggregate all available information  except  that contained in liquidity demand.
['Nicolas S. Lambert', 'Michael Ostrovsky', 'Mikhail Panov']
Strategic trading in informationally complex environments