AI 中文总结
研究含合同设计的拍卖模型，投标人质量投资存在道德风险。通过设计转移规则激励其高投入，考虑二价和一价拍卖，证明有对称贝叶斯纳什均衡，得出最优奖励因子，表明合同使用能提高拍卖人收益，且与拍卖规则无关。
AI 中文摘要
我们考虑一种新的拍卖模型，其中投标人的效用和拍卖人的收入取决于由投标人的成本高昂且具策略性的投资所决定的交易质量因素。该模型的应用包括广告拍卖、政府特许权和众包竞赛等。关键在于，投标人提高质量的努力往往是在分配之前产生的沉没成本，这引发了一个基本的道德风险问题，即失去拍卖的风险会阻碍投资。本文研究了融入拍卖的收益最大化合同设计：拍卖人承诺一个转移规则，根据事后实现的交易质量奖励获胜者，以激励更高的努力。我们的新框架是拍卖理论和委托 - 代理模型的自然推广。我们考虑了第二价格和第一价格拍卖，证明了两种拍卖中都存在自然对称贝叶斯纳什均衡。假设投标人遵循这些自然均衡且投标人数量众多，我们研究线性合同并得出使拍卖人收益最大化的转移规则的最优奖励因子。主要结果表明，随着投标人数量增加，最优奖励因子收敛于拍卖人从质量中获得的边际收益，即拍卖人将质量价值完全传递给获胜者是最优的。这一观察结果在很大程度上与所使用的拍卖规则无关，我们推导了收益等价定理，表明只要存在对称贝叶斯纳什均衡，收益就保持不变。最后，通过与不使用质量奖励的标准拍卖进行定量比较，我们表明合同的使用通过激励投标人进行高投资有效地提高了收益。
英文摘要
We consider a new auction model where the bidders' utilities and the auctioneer's revenue depend on a quality factor of the transaction determined by costly and strategic investments of the bidders. Applications of our model include ad auctions, government concessions and crowdsourcing contests. Crucially, these quality-enhancing efforts made by the bidders are often sunk costs incurred prior to the allocation, creating a fundamental moral hazard problem where the risk of losing the auction discourages investments. In this paper, we study the design of revenue-maximizing contracts integrated into auctions: the auctioneer commits to a transfer rule that rewards the winner for the ex-post realized quality of the transaction to incentivize higher effort. Our new framework is a natural generalization of both the auction theory and the principal-agent model. We consider both the second-price and the first-price auctions. We show that natural symmetric Bayes Nash equilibria exist in both auctions. Assuming these natural equilibria are played by the bidders and the number of bidders is large, we study linear contracts and derive the optimal reward factor of the transfer rule that maximizes the auctioneer's revenue. As the main result, we show that the optimal reward factor converges to the auctioneer's marginal benefit from the quality, as the number of bidders grows. That is, it is optimal for the auctioneer to fully pass through the quality value to the winner. This observation is largely independent of the auction rule used: we derive a revenue equivalence theorem showing that the revenue remains the same as long as symmetric Bayes Nash equilibria exist. Lastly, by quantitatively comparing with the standard auctions where no quality reward is used, we show that the use of contracts effectively improves the revenue by incentivizing high investments from the bidders.
CommentsAccepted at WINE'26
