论文标题
多单位先知不平等的静态定价
Static pricing for multi-unit prophet inequalities
论文作者
论文摘要
我们研究了一个定价问题，卖方有$ k $相同的产品副本，买家依次到达，卖方价格旨在最大程度地提高社会福利。当$ k = 1 $时，这就是所谓的“先知不平等”问题，其中有一个简单的定价方案达到了$ 1/2 $的竞争比率。另一方面，随着$ k $的无限，静态和自适应定价的渐近性能是充分了解的。 我们为小型供应政权提供静态定价计划：$ k $很小，但大于$ 1 $。在我们的工作之前，以这种环境所知的最佳竞争比率是单一先知不平等的$ 1/2 $。我们的定价方案易于描述和实用 - 它是匿名，不自适应和订单的。我们选择一个单一的价格，以均衡售出的商品的预期分数以及在向所有客户提供之前供应不售出的可能性；然后将这个价格提供给每个客户，而供应持续。这扩展了塞缪尔·卡恩（Samuel-Cahn）引入的方法，以$ k = 1 $。该定价计划达到了竞争比率，随着供应的逐渐增加。随后的江，马萨诸塞州和张的工作表明，我们的定价计划是每一个价值$ k $的最佳静态定价。
We study a pricing problem where a seller has $k$ identical copies of a product, buyers arrive sequentially, and the seller prices the items aiming to maximize social welfare. When $k=1$, this is the so called "prophet inequality" problem for which there is a simple pricing scheme achieving a competitive ratio of $1/2$. On the other end of the spectrum, as $k$ goes to infinity, the asymptotic performance of both static and adaptive pricing is well understood. We provide a static pricing scheme for the small-supply regime: where $k$ is small but larger than $1$. Prior to our work, the best competitive ratio known for this setting was the $1/2$ that follows from the single-unit prophet inequality. Our pricing scheme is easy to describe as well as practical -- it is anonymous, non-adaptive, and order-oblivious. We pick a single price that equalizes the expected fraction of items sold and the probability that the supply does not sell out before all customers are served; this price is then offered to each customer while supply lasts. This extends an approach introduced by Samuel-Cahn for the case of $k=1$. This pricing scheme achieves a competitive ratio that increases gradually with the supply. Subsequent work by Jiang, Ma, and Zhang shows that our pricing scheme is the optimal static pricing for every value of $k$.
