In this paper, we study bidding behavior by firms in beauty-contest auctions, i.e. auctions in which the winning bid is the one which gets closest to some function (average) of all submitted bids. Using a dataset on public procurement beauty-contest auctions in Italy and exploiting a change in the auction format, we show that firms' observed biddin behavior departs from equilibrium and can be predicted by an index of sophistication, which captures the firms' accumulated capacity of bidding well (i.e. close to optimality) in the past. We show that our empirical evidence is consistent with a Cognitive Hierarchy model of bidders' behavior. We also investigate whether and how firms learn to think and bid strategically through experience
