Strong Duality for a Multiple-Good Monopolist
Strong Duality for a Multiple-Good Monopolist
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DOI：
10.1145/2764468.2764539
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发表时间：
2014-09
期刊：
影响因子：
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通讯作者：
C. Daskalakis;Alan Deckelbaum;Christos Tzamos
中科院分区：
文献类型：
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作者：
C. Daskalakis;Alan Deckelbaum;Christos Tzamos
我们提供了一个基于双重性的框架，在多好的垄断收入最大化。我们的框架表明，每个最优机制都有一个最优性证书，采取措施之间的最优运输图的形式。使用我们的框架，我们证明了大捆绑机制是最优的当且仅当两个随机优势条件之间的具体措施引起的买方的类型分布。这一结果加强了文献中的几个结果，其中只有充分条件的大捆绑最优性已被提供。作为我们对大捆绑最优性的严格表征的推论，我们证明了每个在[c; c + 1]上支持的n个独立均匀项的最优机制是大捆绑机制，只要c足够大，扩展了巴甫洛夫对2项的结果[Pavlov 2011]。令人惊讶的是，我们的特征还意味着，对于所有c和所有足够大的n，支持[c; c + 1]的n个独立统一项的最佳机制不是大捆绑机制。大捆绑最优性的必要和充分条件是我们更一般的表征结果的一个特例，该结果为任意类型分布的任意机制的最优性提供了必要和充分条件。
We provide a duality-based framework for revenue maximization in a multiple-good monopoly. Our framework shows that every optimal mechanism has a certificate of optimality, taking the form of an optimal transportation map between measures. Using our framework, we prove that grand-bundling mechanisms are optimal if and only if two stochastic dominance conditions hold between specific measures induced by the buyer's type distribution. This result strengthens several results in the literature, where only sufficient conditions for grand-bundling optimality have been provided. As a corollary of our tight characterization of grand-bundling optimality, 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 2011]. Surprisingly, 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. The necessary and sufficient condition for grand bundling optimality is a special case of our more general characterization result that provides necessary and sufficient conditions for the optimality of an arbitrary mechanism for an arbitrary type distribution.