论文标题
销售（大约）最佳的完整信息吗？
Is Selling Complete Information (Approximately) Optimal?
论文作者
论文摘要
我们研究向数据购买者出售信息的问题，该数据购买者在不确定性下面临决策问题。我们考虑了[Blackwell，1951，1953]率先提出的经典贝叶斯决策理论模型。最初，数据购买者只有有关与回报与世界相关状态的部分信息。数据卖家提供有关世界状况的其他信息。该信息是通过信号方案揭示的，也称为实验。在单一代理设置中，任何机制都可以表示为实验菜单。 [Bergemann等，2018]在二元状态和二元行动环境中，介绍了收入最佳机制的完整表征。相比之下，没有任何动作的情况都不知道任何表征。在本文中，我们考虑了更多的一般环境，并且可以说是最简单的机制，该机制仅销售完全有用的实验。在具有二进制状态和$ M \ geq 3 $动作的环境中，我们仅通过出售充分的信息实验来提供$ o（m）$ - 近似最佳收入，并表明近似比率紧密至绝对恒定因素。我们下边界的一个重要必然的推论是，最佳菜单的大小必须至少在可用动作的数量中线性增长，因此在一般的单维设置中，最佳菜单的大小不存在通用上限。 对于多维环境，我们证明，即使可以说，即使是具有3个州和3个动作的最简单匹配的实用环境，最佳收入和收入之间的比率也只能出售完全有用的实验，可以立即增长到代理类型数量的多项式。尽管如此，如果分布统一，我们表明仅出售完全有用的实验确实是最佳机制。
We study the problem of selling information to a data-buyer who faces a decision problem under uncertainty. We consider the classic Bayesian decision-theoretic model pioneered by [Blackwell, 1951, 1953]. Initially, the data buyer has only partial information about the payoff-relevant state of the world. A data seller offers additional information about the state of the world. The information is revealed through signaling schemes, also referred to as experiments. In the single-agent setting, any mechanism can be represented as a menu of experiments. [Bergemann et al., 2018] present a complete characterization of the revenue-optimal mechanism in a binary state and binary action environment. By contrast, no characterization is known for the case with more actions. In this paper, we consider more general environments and study arguably the simplest mechanism, which only sells the fully informative experiment. In the environment with binary state and $m\geq 3$ actions, we provide an $O(m)$-approximation to the optimal revenue by selling only the fully informative experiment and show that the approximation ratio is tight up to an absolute constant factor. An important corollary of our lower bound is that the size of the optimal menu must grow at least linearly in the number of available actions, so no universal upper bound exists for the size of the optimal menu in the general single-dimensional setting. For multi-dimensional environments, we prove that even in arguably the simplest matching utility environment with 3 states and 3 actions, the ratio between the optimal revenue and the revenue by selling only the fully informative experiment can grow immediately to a polynomial of the number of agent types. Nonetheless, if the distribution is uniform, we show that selling only the fully informative experiment is indeed the optimal mechanism.
