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Abstract We study the efficiency of the uniform auction as an allocation mechanism for emission permits among polluting firms. In our model, firms have private information about their abatement costs, which differ across firms and across units, and bidders’ demands are linear. We show that there is a continuum of interior Bayesian Nash equilibria, and only one is efficient, minimizing abatement costs. We find that the existence of many bidders is not a sufficient condition to guarantee an efficient equilibrium in the uniform auction. Additionally, bidders’ types have to be uncorrelated.