增价拍卖中投标者跳跃报价策略研究
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摘要
已有文献对跳跃报价的动机进行了解释,并指出投标者的跳跃报价策略会对拍卖均衡和收益产生影响。本文在对现有文献进行综述基础上,发现跳跃报价策略对拍卖的收益效应依赖于于不同的拍卖分析框架,即拍卖经济模型。由此,本文首先将拍卖经济模型归纳为独立私人价值模型、关联价值模型和共同价值模型三种类型,然后重点结合私人价值模型和关联价值模型,研究了跳跃报价策略对单物品拍卖收益的影响效应,最后在独立私人价值模型下研究了跳跃报价策略对多物品拍卖收益的影响。通过上述研究,得到如下创新性结论。
(1)本文在私人价值模型假设下,考察了单物品增加拍卖中的跳跃报价策略。假设拍卖方打算出售一件不可分离物品且其对该物品的估价为0,即意味着她愿意接受任何严格为正的报价;拍卖方面对由一个特殊投标者和n个一般投标者所构成的n +1个投标者。特殊投标者对物品的估价服从两个非交叉区间上的分布,而每个一般投标者对物品的估价则服从连续可微且相互独立的分布;跳跃报价策略所包含的信息必须足以导致其他投标者投标行为产生分离变化。对于单物品拍卖情形,本文通过证明得出:仅当投标者的估价分布满足一定的严格条件且其身份被隐藏时,跳跃报价方能为其带来利润;拍卖方隐藏的信息越多,投标者为传递其高估价信息而愿意采取的跳跃报价越高且跳跃报价均衡集越大。
(2)本文在关联价值模型假设下,求解了单物品增价拍卖中的跳跃报价均衡。通过证明得出:在均衡处,跳跃报价作为关联工具以选择随后出现的非对称投标函数;每个可能偏离增价拍卖对称均衡的跳跃投标都为投标者提供了一个帕累托改进;均衡的扩展集可能逼近于第一价格或第二价格结果且所产生的预期价格集恰好位于这两个边界之间。
(3)本文在私人价值模型假设下,考察了多物品增价拍卖中的跳跃投标策略。通过推导得到:特殊投标者通过跳跃报价改善其收益的临界值处,当特殊投标者的估价高于临界值时,其将选择跳跃报价,而当其估价低于临界值时,跳跃报价不会发生,特殊投标者将依最小出价增量来出价。并通过一个算例验证了跳跃投标对投标者期望收益的改善取决于投标者的不耐心程度和估价分布。
Previous literatures have discussed the motivation of jump bidding and shown the strategy of bidders’jump bidding would affect the equilibrium and revenue of ascending auctions. On the basis of the review of former literatures, this paper finds that the effect of jump bidding strategy on auction revenue depends on different auction framework or economic models of auction. Thus, firstly this paper divides the economic models of auctions into three different kinds: independent private value model, affliated value model and common value model. Secondly, this paper discusses the effect of jump bidding strategy on one-object auction revenue under the independent private value and affliated value models. Finally, the effect of jump bidding strategy on multiple-object auction revenue under the independent private value model is discussed. Based on the afore-mentioned studies, this paper gets main innovative conclusions as follow.
(1)Basing on the assumptions of independent private value model, the jump bidding strategy is discussed in the paper. There is one seller who wishes to sell a single non-divisable object. We assume that the seller’s valuation for the object is zero which implies she is willing to accept any strictly positive bid. The seller faces n+1 bidders; one of them we refer to as the special bidder and the others we call ordinary bidders. The special bidder draws her valuation from the distribution with a support over two non-overlapping intervals. Each ordinary bidder draws her valuation independently from the continuously differentiable distribution. The information contained in a jump bid must be sufficient to induce a discrete change in the bidding behaviour of the other bidders. We show that in a one-object auction a bidder benefits from jump bidding only if her distribution satisfies certain restrictive conditions and bidder identity is concealed. The more information that a seller conceals, the higher the jump bid a bidder is willing to make in order to signal her valuation and the larger is the set of jump bid equilibria.
(2)This paper solves for equilibria for ascending auctions with affiliated values when jump bidding strategies may be employed to intimidate one’s opponents. In these equilibria, jump bids serve as correlating devices which select asymmetric bidding functions to be played subsequently. Each possibility of jump bidding provides a Pareto improvement for the bidders from the symmetric equilibrium of a sealed bid, second-price auction. The expanded set of equilibria can approximate either first-price or second-price outcomes or produce exactly the set of expected prices between those two bounds.
(3)In an auction for multiple items, the jump bid signals a high valuation by the jump bidder. This causes a discrete change in the bidding behaviour of the other bidder since it causes this bidder to reduce her demand. In both a one-object and multiple-object auctions, a seller may expect less revenue in a jump bid equilibrium than a non-jump bid equilibrium.
(1)本文在私人价值模型假设下,考察了单物品增加拍卖中的跳跃报价策略。假设拍卖方打算出售一件不可分离物品且其对该物品的估价为0,即意味着她愿意接受任何严格为正的报价;拍卖方面对由一个特殊投标者和n个一般投标者所构成的n +1个投标者。特殊投标者对物品的估价服从两个非交叉区间上的分布,而每个一般投标者对物品的估价则服从连续可微且相互独立的分布;跳跃报价策略所包含的信息必须足以导致其他投标者投标行为产生分离变化。对于单物品拍卖情形,本文通过证明得出:仅当投标者的估价分布满足一定的严格条件且其身份被隐藏时,跳跃报价方能为其带来利润;拍卖方隐藏的信息越多,投标者为传递其高估价信息而愿意采取的跳跃报价越高且跳跃报价均衡集越大。
(2)本文在关联价值模型假设下,求解了单物品增价拍卖中的跳跃报价均衡。通过证明得出:在均衡处,跳跃报价作为关联工具以选择随后出现的非对称投标函数;每个可能偏离增价拍卖对称均衡的跳跃投标都为投标者提供了一个帕累托改进;均衡的扩展集可能逼近于第一价格或第二价格结果且所产生的预期价格集恰好位于这两个边界之间。
(3)本文在私人价值模型假设下,考察了多物品增价拍卖中的跳跃投标策略。通过推导得到:特殊投标者通过跳跃报价改善其收益的临界值处,当特殊投标者的估价高于临界值时,其将选择跳跃报价,而当其估价低于临界值时,跳跃报价不会发生,特殊投标者将依最小出价增量来出价。并通过一个算例验证了跳跃投标对投标者期望收益的改善取决于投标者的不耐心程度和估价分布。
Previous literatures have discussed the motivation of jump bidding and shown the strategy of bidders’jump bidding would affect the equilibrium and revenue of ascending auctions. On the basis of the review of former literatures, this paper finds that the effect of jump bidding strategy on auction revenue depends on different auction framework or economic models of auction. Thus, firstly this paper divides the economic models of auctions into three different kinds: independent private value model, affliated value model and common value model. Secondly, this paper discusses the effect of jump bidding strategy on one-object auction revenue under the independent private value and affliated value models. Finally, the effect of jump bidding strategy on multiple-object auction revenue under the independent private value model is discussed. Based on the afore-mentioned studies, this paper gets main innovative conclusions as follow.
(1)Basing on the assumptions of independent private value model, the jump bidding strategy is discussed in the paper. There is one seller who wishes to sell a single non-divisable object. We assume that the seller’s valuation for the object is zero which implies she is willing to accept any strictly positive bid. The seller faces n+1 bidders; one of them we refer to as the special bidder and the others we call ordinary bidders. The special bidder draws her valuation from the distribution with a support over two non-overlapping intervals. Each ordinary bidder draws her valuation independently from the continuously differentiable distribution. The information contained in a jump bid must be sufficient to induce a discrete change in the bidding behaviour of the other bidders. We show that in a one-object auction a bidder benefits from jump bidding only if her distribution satisfies certain restrictive conditions and bidder identity is concealed. The more information that a seller conceals, the higher the jump bid a bidder is willing to make in order to signal her valuation and the larger is the set of jump bid equilibria.
(2)This paper solves for equilibria for ascending auctions with affiliated values when jump bidding strategies may be employed to intimidate one’s opponents. In these equilibria, jump bids serve as correlating devices which select asymmetric bidding functions to be played subsequently. Each possibility of jump bidding provides a Pareto improvement for the bidders from the symmetric equilibrium of a sealed bid, second-price auction. The expanded set of equilibria can approximate either first-price or second-price outcomes or produce exactly the set of expected prices between those two bounds.
(3)In an auction for multiple items, the jump bid signals a high valuation by the jump bidder. This causes a discrete change in the bidding behaviour of the other bidder since it causes this bidder to reduce her demand. In both a one-object and multiple-object auctions, a seller may expect less revenue in a jump bid equilibrium than a non-jump bid equilibrium.
引文
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