A one period model of a speculative market is analyzed in which a monopolistically privately informed trader strategically exploits his information through trade with a market maker. Both the informed trader and the market maker entertain doubts about the uniqueness of the insider's information. I numerically solve for a linear approximate equilibrium in which uncertainty about the number of informed traders in the market plays a dual role. First, it acts as an additional source of noise in the market. Second, it changes the implicit level of competition in the market. Depending on parameter values, these two effects may impact equilibrium characteristics in like or opposite direction. On balance I find: (i) the intensity of an insider's trading is monotonically decreasing in the likelihood that his information is non-unique; (ii) market liquidity increases in the insider's uncertainty and can decrease in the implied level of competition; (iii) expected monopolist insider profits are higher on average that if the insider's information were known to be unique; and )iv) prices tend to be more efficient than in the case of a known monopolist insider.
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