**Market
Microstructure with Uncertain Information Precision: A New Framework**

**Abstract**

This paper provides the financial market microstructure literature with a relatively simple framework to accomodate the possibility for the precision of information to be random. Indeed, many researchers have discovered that the usual normal/exponential framework used in asymmetric information models is intractable when the precision of information is random. This is why we introduce a setting similar to that of Glosten and Milgrom (1985) in which shares of a risky asset can only be traded one at a time. We find that the bid-ask spread and insider profits both increase with a first-order stochastic shift of the information precision, but decrease with a second order stochastic shift. On the other hand, the effect of these stochastic shifts on trading volume is in general ambiguous, since such shifts produce two counter-balancing effects. However, conditions are derived in which the net effect is known. Also, the model's conclusions are shown to be robust to settings that allow for multiple trade sizes, insider risk aversion, elacticity of liquidity trader demand, and market power of the market-maker. The problem solved in this paper is in fact part of a more general problem of uncertain trader characteristics, which has been largely neglected by the financial economics literature. Indeed, financial economists always assume that the characteristics of traders (risk aversion, wealth, information distribution) are common knowledge. Our study is therefore a first step towards understanding the effects of uncertain trader characteristics on financial markets.

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