Abstract
Auction theory is generalized by allowing the number of bidders to be stochastic. In a first-price sealed-bid auction with bidders having constant absolute risk aversion, the expected selling price is higher when the bidders do not know how many other bidders there are than when they do know this. Thus the seller should conceal the number of bidders if he can. Moreover, a bidder's ex ante expected utility is the same whether or not there is a policy of concealing the number of bidders: concealment therefore Pareto-dominates announcement. With risk-neutral bidders, the optimal auction is the same whether or not the bidders know who their competitors are.
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