Can level-k reasoning explain bidding in auctions?

Following the success of level-k reasoning at explaining behaviour in a variety of settings, theorists have begun to apply the level-k model to auctions. While level-k theory is reasonably well developed, there are few empirical tests of the theory in the literature, and those tests that do exist fail to sharply distinguish the theory from its leading rival, Bayesian Nash Equilibrium. In this talk, I show how the predictions of the theories can be disentangled through asymmetric, sequential and all-pay auctions. Using a variety of experimental datasets, I then ask which theory (if either) can explain observed bidding behaviour.