带有反比佣金率和保留价的拍卖模型研究

Study of an auction model with both a reserve price and an inverse commission rate

研究了带有反比佣金率和保留价的密闭式拍卖模型。给出了一般分布下的一级价格密封式拍卖和二级价格密封式拍卖的均衡投标策略;分别求出了在两种拍卖模式中投标人、卖方和拍卖行的预期收益;进一步考察了反比佣金率的系数以及保留价分别对均衡投标策略以及对卖方、投标人和拍卖行三方预期收益的影响。研究结果表明,卖者的预期收益与k及保留价r均成正相关;投标者的预期收益和k成正比,和r成反比。

In order to reflect the actual situation,this paper reports a study of a sealed-bid auction model with both a reserve price and an inverse commission rate. Firstly,we find the equilibrium bidding strategy in both first-price and second-price sealed-bid auctions. Secondly,we obtain the expected revenue of the bidder,seller and auction house,then these results are compared using two models—one with a fixed commission rate and the other without a commission rate. Thirdly,we study the influence of the reserve price and the coefficient in the inverse commission rate on the equilibrium bidding strategy,and on the expected revenues of the bidder,seller and auction house. The results indicate that the expected revenue of the seller has a positive correlation with both r and k,whereas the expected revenue of the bidder has a positive correlation with k but a negative correlation with r.