基于幂效用函数的多属性英式拍卖研究

以采购问题为背景研究多属性拍卖问题，其中拍卖问题的特点是：（1）包含任意有限个属性；（2）买卖双方的效用函数均具有加性结构，且在除价格以外的单个属性上，买方的效用函数和卖方的成本函数均为一般幂函数形式。首先，设计了一种买方事先公布评分函数而卖方轮流提交投标的多属性英式拍卖机制；其次，在卖方对称的假设下分析了拍卖机制中的最优投标策略，确定了最优投标价格和最优非价格属性值；然后，分析得出了最具成本优势的卖方最终胜出的条件以及最优多属性投标；最后，计算了该拍卖机制中买方的期望收益，并求出了使其期望收益最大化的最优评分函数权重。

Research on Multi-attribute English Auction based on Power Utility functions

In this paper,multi-attribute auction is studied in the context of procurement. The considered auction problem has the following two characteristics. One is that the auction contains any finite attributes,conother one is that the utility functions of the auctioneer and the bidders are additive power functions. Firstly, a multi-attribute English auction is designed in which the auctioneer announce the scoring function in advance and the bidders submit bids one by one. Secondly, the optimal bidding strategy of the bidders is analyzed based on the assumption that bidders are symmetry. The optimal bidding price and the optimal values of the non-price attributes are determined. Thirdly, it is proved that the bidder with the lowest cost will win at last only if the minimal increment is small enough. Furthermore, the winning bid can be predicted. At last, the expected payoff of the buyer in the proposed auction is estimated. From the buyer's point of view, the optimal values of the announced weights of the scoring function are calculated.