Oligopoly models of short-run price competition predict that large firms can exercise market power and generate inefficiencies. Inefficiency, however, can arise from other sources as well, such as from heterogeneity in strategic sophistication. We study such a setting in the Texas electricity market, in which bidding behavior of some firms persistently and significantly deviates from Nash-equilibrium bidding. We use information on bids and valuations to estimate the level of strategic sophistication of specific firms in the market. We do this embedding a Cognitive Hierarchy model into a structural model of bidding into auctions. We show that strategic sophistication increases with the size of the firm and it is also related to managers’ educational backgrounds. We then use our model to perform counterfactual calculations about market efficiency under different scenarios that increase strategic sophistication of low-type firms either exogenously or through mergers with more sophisticated firms.