We consider a dynamic equilibrium model of high frequency trading (HFT). The model is a stochastic sequential game with endogenous trading decisions in a limit order market. There are two types of agents: fast and slow traders. Fast traders have speed advantages in terms of analysing information and the low-latency transmission of orders. Nevertheless, slow traders can observe and learn from the signals disclosed by fast traders in the market activity. We find that HFT improves market quality by increasing informational efficiency and liquidity. Fast traders make larger average trading profits than slow traders; however the trading profits of slow traders are higher when there is HFT in the market than in the case where HFT is absent. This is due to both the improvements in market quality induced by HFT and the learning process followed by slow traders, which increases the effectiveness of their trading strategies. We report that a cancellation fee, which has already been imposed by some exchanges, may affect negatively the market quality. Finally, we show that HFT traders may have incentives to manipulate market volatility since they can make larger profits through limit orders when we simulate a volatility shock. . 4 In addition, traders can re-enter at the market multiple times to revise and to modify previous trading strategies. However, agents 2 The fundamental value of the asset can be thought of as the discounted value of expected future dividends. 3 This assumption is supported by previous empirical studies on HFT, which show that fast traders are better informed than other market participants (see, e.g., Hendershott and Riordan, 2010;Brogaard, 2010;Kirilenko et al., 2011; and Brogaard et al., 2011). In addition, similar assumptions have already been used in HFT theoretical models by Biais et al. (2012a), Foucault et al. (2012, and Martinez and Roşu (2011). 4 The expected time between arrivals for high frequency traders is lower than for slow traders, since the expected value of an exponentially distributed variable , , with parameter is 1/ .3 cannot instantaneously modify trading decisions due to the fact that cognition limits prevent them from continuously monitoring the market; thus trading plans are 'sticky' (see, e.g., Biais et al., 2012b). Nevertheless, high frequency traders have the possibility of evaluating market changes and modifying previous trading strategies much faster than slow traders. Thus, fast traders and slow traders re-enter at the market according to two Poisson processes at rate and , respectively, where .Currently, the exchanges in which we can find HFT are fully, or at least partially, organized as limit order markets (e.g. BATS U.S. stock exchange, NYSE, NASDAQ, London Stock Exchange, NYSE Euronext, BATS Chi-X Europe). 5 Consequently, the microstructure features and particularities of these types of trading venues should be considered when evaluating the effects of HFT on market quality and stability. 6 Therefore, we consider a limit order market in our dynamic equil...