Abstract: In this paper, we examine the first-price and second-price sealed-bid auctions with both commission rate and reserve price, and conclude that: (1) equilibrium bidding strategies are decreasing in commission rate under the two types of auctions; (2) equilibrium bidding strategy is increasing in reserve price under the first-price auction and decreasing in reserve price under the second-price auction; (3) the expected payoff of each bidder is decreasing in both commission rate and reserve price under the first-price auction, and it is independent of commission rate and reserve price under the second-price auction; (4) Revenue Equivalence Theorem still holds; (5) under the two types of auctions, as the commission rate increases, the seller's expected revenue decreases, while the auction house's expected revenue and the total expected revenue of the seller and the auction house may increase or decrease; (6) under the two types of auctions, as the reserve price increases, the seller's expected revenue, the auction house's expected revenue and the total expected revenue of the seller and the auction house may increase or decrease; (7) how to design the optimal reserve price is presented; (8) comparisons between results in this paper and the corresponding ones in previous literature are made.

Key words: auction, commission rate, reserve price