In an imperfectly competitive market, we find that an institutional investor with an information advantage consistently earns higher expected trading profits than sophisticated individual investors who internalize their price impact. However, when noise-trading volume and the noise-to-signal ratio are sufficiently high, the institutional investor underperforms naive individual investors who act as price-takers. The aggressive trading behavior of naive investors, driven by their failure to account for price impact, forces the institutional investor to reduce his trading aggressiveness. Our findings highlight that, under certain conditions, the irrationality of naive traders can erode the advantages of information-driven trading strategies.