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In this paper, we explore the consequences of using equilibrium models of auctions in making policy recommendations, such as the design of real world markets, or as a basis for structural estimation when bidders make small errors in optimization. We consider two types of error prone behavior that nest Bayes-Nash equilibrium as a special case. The first is the logit equilibrium model of McKelvey and Palfrey (1995) where bidders measure their payoffs imperfectly. The second is a submission error model where bidders submit an unintended bid with positive probability. First, we establish that when the number of bidders is sufficiently large, even if bidders maximize expected profits to within a few cents, the predictions of the logit equilibrium model can differ greatly from the predictions of a Bayes-Nash equilibrium model. Second, we demonstrate that if we structurally estimate the model assuming that bidders are playing a Bayes-Nash equilibrium when instead they are acting according to the error submission model, we will tend to overestimate markups. Third, we use standard methods to non-parameterically estimate structural auction models on an experimental data set. We find that in experiments where the average valuation for the object being auctioned is fifteen dollars, bidders are within twenty cents of maximizing profits on average. However, in one of the experiments, the non-parameteric estimate of average markups is 40 percent while the true value is 20 percent. We conclude that it is important to conduct sensitivity analysis to determine how robust policy recommendations and parameter estimates are to a priori plausible amounts of error prone behavior.
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