Abstract: Randomized auctions with priority option may be applied in scenarios where a small number of bidders value an item much higher than other bidders. In an auction of an advertising impression, an advertising platform may compute a priority price to be paid by an advertiser who wins a priority auction for the impression. The advertising platform may collect bids from multiple advertisers, and may determine, based on the bids or on election indications from the advertisers, whether to enter any advertisers into the priority auction. In the priority auction, the impression may be allocated to the advertiser with the highest bid, who may be charged at least the priority price. If no advertisers enter the priority auction, the impression may be allocated randomly between the advertisers with the top d bids, and the advertiser winning the randomized secondary auction may be charged a payment amount equal to the (d+1)-th bid.