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本文在扩展的独立私有价值模型下,考虑第二价格和第一价格拍卖机制下的串通出价行为和卖方对串通出价的反映。第二价格串通出价机制和第一价格串通出价机制分别为在这两种拍卖机制下的激励相容、有效的直接显示串通出价机制。我们发现卖方若知道有串通行为,可以提高保留价来减少损失。由于卖方一般情况下不太可能确定是否存在串通行为及参与串通的人数k,但可以确定给定保留价时串通人数的’最优反应’,在第二价格串通出价机制下,给定串通人数,增加保留价可以提高卖方的期望收益,对于确定的保留价,串通人数的增加会减少卖方的期望收益。从而存在这样的纳什均衡:所有的投标人串通,即,k=N,而卖方宣布与之相应的保留价r (N)。当然,并不是所有的串通出价对投标人都是有利可图的,在第一价格拍卖机制下,若卖方可以调整保留价,只有当参与竞投的人很多时,串通出价才有利可图。
Under the extended independent private value model, this paper considers collusion bidding under the second price and the first price auction mechanism and the seller’s reflection on collusive bidding. The second price collusive bidding mechanism and the first price collusive bidding mechanism are incentive-compatible and effective direct collusion bidding mechanisms under the two auction mechanisms respectively. We find that if the seller knows that there is collusive behavior, the seller can raise the reserve price to reduce the loss. Since it is not possible for the seller to determine, in general, whether there is collusion and the number of persons involved in collusion k, the ’optimal response’ to the number of collusion given a reserve price can be determined. Given the collusion bidding mechanism under the second price collation , Increasing the reserve price can increase the expected return of the seller, and increasing the collusion for a given reserve price will reduce the seller’s expected return. Thus there is such a Nash equilibrium that all bidders collude, that is, k = N, and the seller declares a reserve price r (N) corresponding thereto. Of course, not all collusive bidders are profitable to bidders. Under the first price auction mechanism, if the seller can adjust the reserve price, the collusive bid can only be profitable if there are many bidders.