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.

This paper investigates how noise trading behavior is influenced by limited attention. As the daily price limit rules of the Chinese stock market provide a scenario for the exhibition of salient payoffs, speculators elevate prices to attract noise traders into the market. Utilizing a series of distraction events stemming from mobile games as exogenous shocks to investors’ attention, we find that the gambler-like behavior, termed as “Hitting game” is crowded out. Consistent with our attention mechanism, indicators such as trading volume decline in response to these game shocks.

We hypothesize and test an inverse relationship between liquidity and price volatility derived from microstructure theory. Two important facets of liquidity trading are examined: thickness and noisiness. As represented by expected volume (thickness) and realized average commission cost per share (noisiness) of NYSE equity trading, both facets are found negatively associated with ex post and ex ante price volatilities of the NYSE stock portfolios and the NYSE composite index futures. Furthermore, the inverse association between volatility and noisiness is amplified in times of market crisis. The overall results demonstrate that volatility increases as noise trading declines. All findings retain statistical significance and materiality after controlling for a number of specifications. This inverse liquidity-volatility relationship reflects a microstructure interpretation of the liquidity risk premium documented in the asset pricing literature.