AI 中文总结
本文针对付费竞标拍卖中失利方支付易受卖家干预的问题，提出目标损失暴露的压力测试方法，推导得出相关暴露前沿结论，明确不同拍卖形式的暴露特性及干预对出价的影响。
AI 中文摘要
付费竞标拍卖在分配前向参与者收费，因此失利方的支付易受卖家干预。本文引入目标损失暴露，这是一种压力测试：当一个指定竞标者的对手的均衡报告被固定在任意高水平、同时保留其类型分布时，记录该指定竞标者的支付。在非负支付以及赢家支付至少等于输家支付的排序条件下，收入等价性得出了由无声消耗战达到的严格双边竞标者边界。对于任意数量的竞标者，该形式在支付排序的局域规则中达到上限。证明过程将支付位置构建为线性规划，并构造了对偶概率测度。当竞标者数量超过2时，互补松弛条件几乎处处确定最优输家支付方案。赢家支付拍卖的暴露为零，标准全支付拍卖的暴露严格低于前沿，且前沿暴露随竞标者数量增加而降低。仅输家规则表明，移除支付排序可使暴露无界。共同冲击扩展结果还显示，预期干预会改变竞标出价，但保留标准形式的排序。这些结果将收入等价性确定的总临时支付与该支付所附着的赢或输状态分离开来。
英文摘要
Pay-to-bid auctions charge participants before allocation and therefore make losing-side payments vulnerable to seller intervention. This paper introduces targeted-loss exposure, a stress test that records a designated bidder's payment when one rival's equilibrium report is fixed at an arbitrarily high level while her type distribution is preserved. Under nonnegative payments and an ordering in which a winner pays at least as much as a loser, revenue equivalence yields a sharp two-bidder bound attained by the silent war of attrition. For any number of bidders, the same format attains the upper bound among payment-ordered rank-local rules. The proof formulates payment location as a linear program and constructs a dual probability measure. With more than two bidders, complementary slackness determines the optimal loser-payment schedule almost everywhere. Winner-pay auctions have zero exposure, standard all-pay auctions lie strictly below the frontier, and frontier exposure decreases as the number of bidders rises. A loser-only rule shows that removing payment ordering can make exposure unbounded. A common-shock extension also shows that anticipating intervention changes bids but preserves the ordering of standard formats. The results separate the total interim payment fixed by revenue equivalence from the winning or losing state to which that payment is attached.
Comments10 pages; includes a technical appendix
