带佣金率和保留价的一级和二级价格拍卖

本文通过引入佣金率和保留价,分别讨论了一级和二级价格密封式拍卖,得到以下结论:(1)两种密封式拍卖的均衡报价随佣金率的提高而减少;(2)一级价格密封式拍卖的均衡报价随保留价的增加而增加,而二级价格密封式拍卖的均衡报价随保留价的增加而减少;(3)一级价格密封式拍卖的投标者预期收益与佣金率和保留价均呈反向变动,而二级价格密封式拍卖的投标者预期收益独立于佣金率和保留价;(4)收益等价定理仍然成立;(5)在两种密封式拍卖中,当佣金率增加时,卖方的预期收益减少,拍卖行的预期收益以及卖方和拍卖行的总预期收益可能增加也可能减少;(6)在两种密封式拍卖中,当保留价增加时,卖方的预期收益、拍卖行的预期收益以及卖方和拍卖行的总预期收益可能增加也可能减少;(7)给出了卖方的最优保留价的表达式;(8)把本文的结论与以前相应的研究工作做了比较。

The First-price and Second-price Auctions with both Commission Rate and Reserve Price

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.