Noise and competition in strategic oligopoly

Focusing on homogeneous beliefs, we can distinguish two commonly shared ideas that, i) the competition between informed traders destroys their trading profits, ii) trading with a noisy signal brings about a loss in the expected profits. So far, it has been proved in the latter framework, that when N strategic and perfectly informed traders compete in the financial market, i) the informativeness of prices increases with the degree of competition and, ii) the aggregate and individual profits go to 0 when N is large. In this paper, we propose a general study where N strategic informaed agents have heterogeneous beliefs, i.e. are endowed with noisy information and compete à la Nash. We prove the existence and uniqueness of a linear equilibrium generalizing Kyle (1985) results to the case of N informed traders when the insiders have heterogeneous beliefs. In this general framework, we derive the following striking results: for certain regions of noise and numbers of competitors in excess of four, i) each individual expected profit is greater than the one obtained in the perfectly informed (and homogeneous beliefs) case; ii) the aggregate profit has a finite (strictly) positive limit when N is large. iii) Even when an infinite number of insiders compete in the market, the price is no longer efficient and does not fully reveal the final liquidation value of the risky asset. iv) In the particular case where each informed agent is endowed with a signal the precision of which is the same, a) we show that there exists an optimal level of noise for which each individual expected profit is maximized; b) we show that there exists an optimal size of the market for which the aggregate expectged profit is maximized; c) the liquidity is an increasing function of the number of informed traders but has a finite limit for large N; d) the informativeness of prices is a decreasing function of the number of informed traders.