abstract High Frequency Trading (HFT) broadly refers to trading strategies involving fast submission, cancelation and revision of orders in a Continuous Double Auction (CDA). Often, a massive number of orders is submitted to be left on the book for very short times and it is estimated that more than 50% of daily stocks are exchanged by HFT financial firms. There is anecdotal evidence that such firms are willing to spend hundreds of millions to increase the speed of their operations by a few milliseconds through the installation of fiber cables in the ocean or purchasing other related IT infrastructure, ([Philips, 2012]). In this paper we describe a stylized model of HFT in which a set of agents want to buy or sell a single stock in a trading session. We assume that the limit price is a simple linear combination of the outstanding best aks and bid at the time of submission, as in ([Ladley and Pellizzari, 2014]). HFT is included in the model allowing some traders to cancel and resubm...