The logic of revenue comparisons for different types of common-value auctions is substantially altered if the number of participants, rather than being fixed, responds endogenously to the expected profitability from participating. In a thoroughly symmetric model, a seller may prefer that competition be indirect: an auction procedure in which fewer participants are needed to drive the expected profitability from participating down to the level obtainable in other auctions in the economy can attain higher expected revenue if a sale is sufficiently likely. This insight allows a complete revenue ranking of standard auction procedures, with endogenous entry.
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