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A Simple and Approximately Optimal Mechanism for an Additive Buyer

机译：简单的，近似最优的加成购买者机制

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We consider a monopolist seller with n heterogeneousitems, facing a single buyer. The buyer hasa value for each item drawn independently according to(non-identical) distributions, and his value for a set ofitems is additive. The seller aims to maximize his revenue.It is known that an optimal mechanism in this setting maybe quite complex, requiring randomization [19] and menusof infinite size [15]. Hart and Nisan [17] have initiated astudy of two very simple pricing schemes for this setting:item pricing, in which each item is priced at its monopolyreserve; and bundle pricing, in which the entire set ofitems is priced and sold as one bundle. Hart and Nisan [17]have shown that neither scheme can guarantee more thana vanishingly small fraction of the optimal revenue. Insharp contrast, we show that for any distributions, thebetter of item and bundle pricing is a constant-factorapproximation to the optimal revenue. We further discussextensions to multiple buyers and to valuations that arecorrelated across items.
机译：我们考虑具有n个异质项的垄断卖方，面对单个买方。买方具有根据（不同）分布独立绘制的每个项目的价值，而他对一组项目的价值是可加的。卖方旨在使自己的收入最大化。众所周知，这种情况下的最佳机制可能非常复杂，需要随机化[19]和无限大小的菜单[15]。 Hart和Nisan [17]已针对这种情况启动了两种非常简单的定价方案的研究：项目定价，其中每个项目均按其垄断储备定价;和捆绑定价，其中整套项目都按捆绑定价并出售。哈特和尼桑[17]表明，这两种方案都不能保证最优收入的很小一部分。 Insharp对比，我们表明，对于任何分配，项目和捆绑定价的最佳选择是最佳收益的恒定因子近似值。我们进一步讨论了扩展到多个买家以及各个项目相关的估值的问题。

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