We introduce a dynamic mechanism design problem in which the designer wants to offer for sale an item to an agent, and another item to the same agent at some point in the future. The agent's joint distribution of valuations for the two items is known, and the agent knows the valuation for the current item (but not for the one in the future). The designer seeks to maximize expected revenue, and the auction must be deterministic, truthful, and ex post individually rational. The optimum mechanism involves a protocol whereby the seller elicits the buyer's current valuation, and based on the bid makes two take-it-or-leave-it offers, one for now and one for the future. We show that finding the optimum deterministic mechanism in this situation - arguably the simplest meaningful dynamic mechanism design problem imaginable - is NP-hard. We also prove several positive results, among them a polynomial linear programming-based algorithm for the optimum randomized auction (even for many bidders and periods), and we show strong separations in revenue between non-adaptive, adaptive, and randomized auctions, even when the valuations in the two periods are uncorrelated. Finally, for the same problem in an environment in which contracts cannot be enforced, and thus perfection of equilibrium is necessary, we show that the optimum randomized mechanism requires multiple rounds of cheap talk-like interactions.

翻译：我们引入了一个动态机制设计问题，其中设计者希望向一个代理人出售一件商品，并在未来的某个时间点向同一代理人出售另一件商品。代理人对两件商品的联合估值分布是已知的，且代理人知道当前商品的估值（但不知道未来商品的估值）。设计者旨在最大化期望收益，并且拍卖必须是确定性的、诚实的以及事后个体理性的。最优机制涉及一个协议，其中卖家诱导买家报出当前估值，并根据报价提供两项“要么接受要么放弃”的报价，一项针对当前，一项针对未来。我们证明，在此情况下找到最优确定性机制——可以说这是能想象到的最简单的有意义动态机制设计问题——是NP难的。我们还证明了几个正向结果，其中包括一个基于多项式线性规划算法的最优随机拍卖（即使针对多个竞拍者和多个时期），并且我们展示了非自适应、自适应和随机拍卖之间在收益上的显著分离，即使两个时期的估值不相关。最后，针对合同无法强制执行且因此需要均衡完美性的同一问题环境，我们证明最优随机机制需要多轮类似廉价的交谈交互。