Sequential elimination in multi-stage all-pay auctions
研究多阶段全支付拍卖中每轮淘汰最低出价者的最优投标策略和卖方期望收益，发现与典型策略相反，最优出价随投标人数增加而递减，且当投标人超过三人时，多阶段拍卖的期望收益低于单阶段拍卖。
I study a multi-stage all-pay auction in which the lowest bidder in each stage is eliminated. Elimination continues until only two bidders remain, one of whom wins the auction. I analyse optimal bidding behaviour and the seller’s expected revenue when bidders have independent and private values. In contrast to typical bidding strategies, the optimal bid in each stage is strictly decreasing in the number of bidders. For a fixed number of bidders, however, bids increase as bidders progress through the stages of the auction. Despite independent values, this multi-stage auction yields less expected revenue to the seller than its single-stage counterpart when there are more than three bidders.