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In this paper, we design and implement an experiment aimed at testing thelevel-k model of auctions. We begin by asking which (simple) environments canbest disentangle the level-k model from its leading rival, Bayes-Nashequilibrium. We find two environments that are particularly suited to thispurpose: an all-pay auction with uniformly distributed values, and afirst-price auction with the possibility of cancelled bids. We then implementboth of these environments in a virtual laboratory in order to see which theorycan best explain observed bidding behaviour. We find that, when plausiblycalibrated, the level-k model substantially under-predicts the observed bidsand is clearly out-performed by equilibrium. Moreover, attempting to fit thelevel-k model to the observed data results in implausibly high estimatedlevels, which in turn bear no relation to the levels inferred from a game knownto trigger level-k reasoning. Finally, subjects almost never appeal to iteratedreasoning when asked to explain how they bid. Overall, these findings suggestthat, despite its notable success in predicting behaviour in other strategicsettings, the level-k model (and its close cousin cognitive hierarchy) cannotexplain behaviour in auctions.

Going... going... wrong: a test of the level-k (and cognitive hierarchy) models of bidding behaviour