This paper introduces reinforcement learning to examine the effect of trading on noise in a dynamic limit order market equilibrium. It shows that intensive noise liquidity provision (consumption) increases speculators' liquidity consumption (provision), improving (reducing) market liquidity. Channeled by uninformed chasing and informed aggressive liquidity provision, the increasing noise liquidity provision and consumption, respectively, improve price efficiency, generating a U-shaped price efficiency to the noise trading uncertainty on liquidity provision and consumption. Associated with a hump-shaped (U-shaped) profitability for the informed (uninformed) at a U-shaped noise trading cost in the noise trading uncertainty, this implies that, at increasing noise trading cost, intensive noise liquidity provision improves market liquidity, price efficiency, order profitability of informed traders, and reduces the loss, even makes profit, for uninformed traders.

We study the influence of investor attention on mutual fund investors' fund selection and fund managers' portfolio choice. Using the Google Search Volume Index to measure investor attention on individual stocks, we find fund investors tend to direct more capital to mutual funds holding more high-attention stocks; fund managers tend to perform window-dressing trading to increase the portfolio holdings of high-attention stocks displayed to investors. Our results suggest that funds, particularly those with strong incentives, strategically trade on stock attention to attract investor flows. This strategic trading behaviour is also associated with fund underperformance and leads to larger non-fundamental volatility of holding stocks.