多善垄断者的强对偶性
Strong Duality for a Multiple-Good Monopolist
摘要：
我们描述了多好垄断问题的最优机制，并提供了一个框架来找到它们。我们表明，一个机制是最优的当且仅当一个措施$μ$来自买方的类型分布满足一定的随机优势条件。这一措施表达了边际变化的卖方收入下边际变化的租金支付给买方类型的子集。作为一个推论，我们的最优性的大捆绑机制的特点，加强文献中的几个结果，只有充分的最优性条件已经得出。作为一个应用，我们表明，$n$独立的统一项目，每个支持$[c,c+1]$的最佳机制是一个大捆绑机制，只要$c$是足够大的，扩展巴甫洛夫的结果$2$项目[巴甫洛夫'11]。同时，我们的特征也意味着，对于所有$c$和所有足够大的$n$，最佳的机制，$n$独立的统一项目支持$[c,c+1]$是不是一个盛大的捆绑机制。
英文摘要：
We characterize optimal mechanisms for the multiple-good monopoly problem and provide a framework to find them. We show that a mechanism is optimal if and only if a measure $μ$ derived from the buyer's type distribution satisfies certain stochastic dominance conditions. This measure expresses the marginal change in the seller's revenue under marginal changes in the rent paid to subsets of buyer types. As a corollary, we characterize the optimality of grand-bundling mechanisms, strengthening several results in the literature, where only sufficient optimality conditions have been derived. As an application, we show that the optimal mechanism for $n$ independent uniform items each supported on $[c,c+1]$ is a grand-bundling mechanism, as long as $c$ is sufficiently large, extending Pavlov's result for $2$ items [Pavlov'11]. At the same time, our characterization also implies that, for all $c$ and for all sufficiently large $n$, the optimal mechanism for $n$ independent uniform items supported on $[c,c+1]$ is not a grand bundling mechanism.
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