Pre-print, Working paper: In this paper, we design and implement an experiment aimed at testing the level-k model of auctions. We begin by identifying (simple) environments that optimally disentangle the predictions of the level-k model from the natural benchmark of Bayes-Nash equilibrium. We then implement these environments within a virtual laboratory in order to see which theory can best explain observed bidding behaviour. Overall, our findings suggest that, despite its notable success in predicting behaviour in other strategic settings, the level-k model (and its close cousin, cognitive hierarchy) cannot explain behaviour in auctions.