In this essay I discuss algorithmic finance, specifically the use of fully automated trading, including high-frequency trading, in the light of Michel Foucault's notion of governmentality. I argue that a governmentality perspective offers a fruitful way of understanding particular aspects of high-frequency trading, such as how algorithms are designed to govern other market participants' anticipations of market dynamics. However, I also argue that, to fully understand the realm of algorithmic finance and high-frequency trading, it is important to supplement a governmentality approach with an analytical lexicon which is not primarily centred on productive forms of power. Specifically, I suggest that, according to media discourses on high-frequency trading, algorithmic finance often works in ways that are better grasped through, e.g. Elias Canetti's work on predatory power and Roger Caillois's work on mimesis.