Abstract
We model endogenous information acquisition in a limit order market for a single financial asset. The asset has a common value; in addition, each trader has a private value for it. Traders randomly arrive at the market, after choosing whether to purchase information about the common value. They may either post prices or accept posted prices. If a trader's order has not executed, he randomly reenters the market, and may change his previous order. The model is thus a dynamic stochastic game with asymmetric information. We numerically solve for the equilibrium of the trading game, and characterize equilibria with endogenous information acquisition. Over a range of information acquisition costs, the game exhibits a prisoner's dilemma - all agents, including those who acquire information, are worse off. Agents with the lowest intrinsic benefit from trade have the highest value for information and also tend to supply liquidity. As a result, market observables such as bid and ask quotes, in addition to transaction prices, are informative about the common value of the asset. Adverse selection is important for individuals (agents have lower payoffs when uninformed), but in the aggregate it has little effect on investor surplus, unless gains to trade are small. Comparisons to a frictionless benchmark show that the limit order market is effective at consummating trade and generating consumer surplus, even in the presence of asymmetric information.
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