In a multi-unit online English auction, the honest bidders can adopt the counteracting bidding strategies to reduce the seller's incentive to shill.However, even we consider the honest bidders'strategic response to shill bidding, the shill bidding is still profitable for the seller.The more effective measures to deter shill bidding may include attracting more potential bidders and limiting the number of items for sale in one auction.We also consider seller's optimal strategic response to the counteracting bidding strategies, and solve seller's optimal shill bidding.The result shows that whether the optimal shill bidding is unique or multiple, the optimal strategy for the seller is to adopt a lower shill bid at the beginning, and then dynamically adjust the shill bid to the optimal level after observing the previous bidding information.%在独立私有价值的多单位网上英式拍卖中,诚实的竞标者能够采用对抗性的竞标策略来降低卖者参与托投标的激励,然而即使考虑了诚实竞标者对于托投标的策略性响应,托投标对于卖者而言依然是有利可图的.更为有效地阻止托投标的措施可能包括吸引更多的潜在竞标者,并限制在单次拍卖中销售的物品数量.同时考虑了卖者对于这种对抗性竞标策略的策略响应,求解了卖者的最优托投标,结论表明无论最优的托投标是唯一的还是多重的,卖者的最优策略是在开始使用低的托投标,在观察到之前的竞标信息之后通过动态调整将托投标设定到最优水平.
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