We consider a monopoly information holder selling information to a budget-constrained decision maker, who may benefit from the seller's information. The decision maker has a utility function that depends on his action and an uncertain state of the world. The seller and the buyer each observe a private signal regarding the state of the world, which may be correlated with each other. The seller's goal is to sell her private information to the buyer and extract maximum possible revenue, subject to the buyer's budget constraints. We consider three different settings with increasing generality, i.e., the seller's signal and the buyer's signal can be independent, correlated, or follow a general distribution accessed through a black-box sampling oracle. For each setting, we design information selling mechanisms which are both optimal and simple in the sense that they can be naturally interpreted, have succinct representations, and can be efficiently computed. Notably, though the optimal mechanism exhibits slightly increasing complexity as the setting becomes more general, all our mechanisms share the same format of acting as a consultant who recommends the best action to the buyer but uses different and carefully designed payment rules for different settings. Each of our optimal mechanisms can be easily computed by solving a single polynomial-size linear program. This significantly simplifies exponential-size LPs solved by the Ellipsoid method in the previous work, which computes the optimal mechanisms in the same setting but without budget limit. Such simplification is enabled by our new characterizations of the optimal mechanism in the (more realistic) budget-constrained setting.

中文翻译：

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通过咨询销售信息

我们考虑垄断信息持有者向预算受限的决策者出售信息，决策者可能会从卖方的信息中受益。决策者的效用函数取决于他的行为和世界的不确定状态。卖方和买方各自观察关于世界状态的私人信号，该信号可能彼此相关。卖方的目标是将她的私人信息出售给买方，并在买方的预算限制下获取最大可能的收入。我们考虑了三种不同的具有越来越普遍性的设置，即卖方的信号和买方的信号可以是独立的、相关的或遵循通过黑盒抽样预言机访问的一般分布。对于每个设置，我们设计的信息销售机制既是最优的又是简单的，因为它们可以被自然地解释，具有简洁的表示，并且可以有效地计算。值得注意的是，尽管随着设置变得更一般，最优机制的复杂性略有增加，但我们所有的机制都具有相同的形式，即充当顾问，向买方推荐最佳行动，但针对不同的设置使用不同且精心设计的付款规则。我们的每个最佳机制都可以通过求解单个多项式大小的线性程序来轻松计算。这显着简化了之前工作中通过 Ellipsoid 方法求解的指数大小的 LP，该方法在相同设置下计算最佳机制，但没有预算限制。