A Theory of Auctions with Endogenous Valuations
研究了多个买家通过花费成本影响自身估价时，卖家如何分配物品以实现收益最大化，发现统一价格拍卖和歧视性拍卖结合反应性保留价是最优对称机制。
We derive the symmetric, revenue-maximizing allocation of several units among agents who take costly actions that influence their values. The problem is equivalent to a reduced-form model where agents have nonexpected utility. The uniform-price auction and the discriminatory pay-your-bid auction with reserve prices that react to both demand and supply constitute symmetric, optimal mechanisms. We also identify a condition under which the overall optimal mechanism is indeed symmetric and illustrate the structure of the optimal asymmetric mechanism when the condition fails. The main tool in our analysis is an integral inequality based on Fan and Lorentz (1954).