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The structural parameters of a share‐auction model accounting for asymmetries across bidders, as well as supply uncertainty, are estimated with a sample of French Treasury auctions. We find evidence of both informational and risk aversion asymmetries across bidders. A counter‐factual analysis also suggests that, in the context of the French Treasury auctions, a shift from the discriminatory to the uniform‐price format would simultaneously benefit the French Treasury and the auctions' participants. Copyright © 2006 John Wiley & Sons, Ltd.