Information and optimal trading strategies with dark pools

We study how asymmetric information affects market participants' choice of trading venue (either an exchange or dark pool), and the optimal submission strategies in a sequential trading game. The exchange is organized as a fully transparent limit order book, and the dark pool is an opaque venue where orders are continuously executed at the midpoint of the bid and ask prices that prevail in the exchange. We find that when the limit order book conveys no information rational uninformed traders never trade in the dark pool due to price risk. However, price risk may be reduced when the information in the book induces an uninformed buyer (seller) to believe that the value of the asset is high (low) since the order was previously submitted by an informed buyer (seller). The optimal strategy of an informed trader takes into account the information leakage, and the strategic response of each type of trader in the subsequent stages. Our main finding is that, adding a dark pool alongside an exchange, may divert the informed trader from the exchange to the dark pool. When the execution risk in the dark pool is low, the informed trader decides to trade in the dark pool. In this case the adverse selection problem in the exchange reduces and consequently, the uninformed trader decides to switch from no trade to placing a limit order in the exchange.