AI 中文总结
本文研究最优信息结构的稀疏性，通过线性规划方法发现其稀疏特性，并在含网络效应的创新采用问题中验证，高状态下确定性推荐全采用，低状态下随机化嵌套行动组合以最大化采用者数量。
AI 中文摘要
本文通过利用信息设计的线性规划公式，揭示了最优信息结构的一般性质。一个关键观察是，最优解可被视为“稀疏的”，即行动-状态联合分布的诸多坐标为零。这意味着，一旦行动-状态组合的一部分被固定，剩余部分的波动空间有限。因此，在许多状态下，代理人的行动推荐是条件确定的，或以一种允许部分代理人推断其他代理人推荐的方式相关。稀疏性的含义在一个采用问题中得到说明，其中设计者最大化具有网络效应的创新的采用者数量。最优信息结构在高状态下确定性地推荐全部采用，而在低状态下则对嵌套行动组合进行随机化，使得每当一个代理人被推荐采用时，她确定更乐观的代理人也会采用。
英文摘要
This paper uncovers general properties of optimal information structures by exploiting a linear-programming formulation of information design. A critical observation is that an optimum can be found as ``sparse,'' i.e., many coordinates of the action-state joint distribution are zero. This implies that, once part of an action-state profile is fixed, there is limited room for the remaining part to fluctuate. As a result, agents' action recommendations are conditionally deterministic in many states, or correlated in a way that allows some agents to infer others' recommendations. The implications of sparsity are illustrated in an adoption problem, where the designer maximizes the number of adopters of an innovation that features network effects. The optimal information structure deterministically recommends full adoption in high states, while it randomizes over nested action profiles in low states, so that whenever an agent is recommended to adopt, she is certain that more optimistic agents also adopt.
