ISER Discussion Paper, Institute of Social and Economic Research, Osaka University 849
We analyze the optimal reserve price in a second price auction when there are N types of bidders whose valuations are drawn from different distribution functions. The seller cannot determine the specific type of each bidder. First, we show that the number of bidders affects the reserve price. Second, we give the sufficient conditions for the uniqueness of the optimal reserve price. Third, we find that if a bidder is replaced by a stronger bidder, the optimal reserve price may decrease. Finally, we give sufficient conditions that ensure the seller will not use a reserve price; hence, the auction will be efficient.