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We analyze competition among informed traders in the continuous-time Kylẽ 1985! model, as Foster and Viswanathan~1996! do in discrete time. We explicitly describe the unique linear equilibrium when signals are imperfectly correlated and confirm the conjecture of Holden and Subrahmanyam~1992! that there is no linear equilibrium when signals are perfectly correlated. One result is that at some date, and at all dates thereafter, the market would have been more informationally efficient had there been a monopolist informed trader instead of competing traders. The relatively large amount of private information remaining near the end of trading causes the market to approach complete illiquidity.HOW WILL AN INVESTOR WITH INFORMATION superior to the market trade? One intuition is that he will trade very aggressively, limited only by risk aversion and margin requirements. Another is that he will moderate his trades so as not to tip his hand too early. The Kyle~1985! model of informed trading supports the latter intuition. The informed trader in Kyle's model, when trading in continuous time, does so in such a way that his information is revealed at a constant rate. The first intuition is supported by Holden and Subrahmanyam~1992!. The difference between the two papers is that Holden and Subrahmanyam assume at least two traders have the same information. Each trader tries to beat the others to the market, with the result that their information is revealed almost immediately.The purpose of this paper is to study the nature of competition between informed traders, and the rate at which information is revealed to the market, when traders may have diverse signals and can trade continuously. The assumption of continuous trading simplifies the solution of the model. We build upon the work of Foster and Viswanathan~1996! and Cao~1995!, who study this model in discrete time.

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This paper analyzes models of securities markets with a single strategic informed trader and competitive market makers. In one version, uninformed trades arrive as a Brownian motion and market makers see only the order imbalance, as in Kyle (1985). In the other version, uninformed trades arrive as a Poisson process and market makers see individual trades. This is similar to the Glosten-Milgrom (1985) model, except that we allow the informed trader to optimize his times of trading. We show there is an equilibrium in the Glosten-Milgrom-type model in which the informed trader plays a mixed strategy (a point process with stochastic intensity). In this equilibrium, informed and uninformed trades arrive probabilistically, as Glosten and Milgrom assume. We study a sequence of such markets in which uninformed trades become smaller and arrive more frequently, approximating a Brownian motion. We show that the equilibria of the Glosten-Milgrom model converge to the equilibrium of the Kyle model. Copyright The Econometric Society 2004.