考虑投标者后悔的一级密封拍卖的最优投标策略

Optimal Bidding Strategy in First-price Sealed Auction Considering the Bidder's Regret

许多实验研究表明,投标者在拍卖过程中表现出的预期后悔心理行为会对投标策略产生影响,在这种情况下如何确定最优投标策略是一个值得关注的问题。针对一级密封拍卖的最优投标策略确定问题,分别采用线性函数和非线性函数刻画投标者的获胜者后悔和失败者后悔心理行为,构建非线性拍卖模型,通过模型求解分析最优投标策略;进一步地,给出确定拍卖模型中描述投标者后悔心理行为参数的实验方法,并通过一个关于SO2排污权拍卖的实例分析说明非线性拍卖模型及实验方法的可行性和潜在应用。研究结果表明,最优投标策略与投标者价值和后悔行为有关;最优投标策略为获胜者后悔参数的减函数,且为失败者后悔参数的增函数;完全理性的最优投标策略是所得最优投标策略的特例;当投标者人数非常多时,完全理性的最优投标策略是报出自身的真实估价;在仅考虑投标者获胜后悔情形下,其最优投标策略与线性拍卖模型所得结果相同,且低于完全理性的最优投标策略;在仅考虑投标者失败后悔情形下,其最优投标策略高于完全理性的最优投标策略;与线性拍卖模型比较,由非线性拍卖模型得到的最优投标策略更接近于真实投标报价。提出的非线性拍卖模型为解决现实拍卖中考虑投标者心理行为的最优投标策略确定问题提供借鉴。

Numerous experimental studies have shown that the bidders usually exhibit the anticipated regret psycological behaviors in first-price sealed auctions and such behaviors will have impacts on the final bidding strategies. Thus, how to determine the op- timal bidding strategy with consideration of the bidder＇s anticipated regret is a noteworthy topic.For the problem of the optimal bidding strategy in first-price sealed auction, a linear function and a non-linear function are adopt- ed to describe the winner regret with respect to paying much higher price than the second highest bid price and the loser regret with respect to missing opportunities to win at a favorable price respectively. On such bases, a non-linear auction model is con- structed. Then, the optimal bidding strategy is analyzed based on the above model. Further, an experimental method is carried out to determine the corresponding parameters for describing the bidder＇s regret behavior. Moreover, a case study in the field of the auctions of SO2 emission permits is introduced to illustrate the feasibility and its potential application of the study.Through the theoretical analysis, we find that the optimal bidding strategy is related to not only the bidder＇s value but also the bidder＇s regret, which bridges the gap between the bidding strategy and the bidder＇s psychological behavior. The optimal bidding strategy is the descending function of the winner regret parameter and the increasing function of the loser regret parameter. In ad- dition, when the bidder＇s regret behavior is not considered, the optimal bidding strategy is the same as the one under the perfect rationality. It means that the optimal bidding strategy under the perfect rationality is a special case of the one determined by the non-linear auction model. In particularly, when the number of bidders is large enough, the optimal bidding strategy under the perfect rationality is just the bidder~ true value. In the situation where the winner regret is considered only but the loser regret is ignored, the optimal bidding strategy is the same as the one determined by the linear auction model and is lower than the one un- der the perfect rationality. Otherwise, the optimal bidding strategy is higher than the one under the perfect rationality. Compared with the optimal bidding strategy determined by the linear auction model, the one determined by the non-linear auction model is much closer to the real auction bid price. The non-linear auction model proposed in this paper provides guidance for determining the optimal bidding strategy in the real auction considering the bidder＇s regret.