具有组合行动的贝叶斯说服策略
Algorithmic Bayesian persuasion with combinatorial actions
摘要：
贝叶斯说服是一种理解战略信息披露的模型：具有信息优势的代理人（称为发送者）通过向另一个代理人（称为接收者）发送信号来战略性地披露信息。在算法贝叶斯说服，我们感兴趣的是有效地设计发送者的信令方案，导致接收者采取有利于发送者的行动。本文研究了算法贝叶斯说服设置，其中接收者的可行行动由组合约束指定，例如，图中的拟阵或路径。我们首先表明，常数因子逼近是NP-困难的，即使在一些特殊情况下的拟阵或道路。然后，我们提出了一个多项式时间算法一般拟阵假设的自然状态的数量是一个常数。最后，我们考虑一个宽松的概念的说服力，称为CCE说服力，并提出了多项式时间逼近的充分条件。
英文摘要：
Bayesian persuasion is a model for understanding strategic information revelation: an agent with an informational advantage, called a sender, strategically discloses information by sending signals to another agent, called a receiver. In algorithmic Bayesian persuasion, we are interested in efficiently designing the sender's signaling schemes that lead the receiver to take action in favor of the sender. This paper studies algorithmic Bayesian-persuasion settings where the receiver's feasible actions are specified by combinatorial constraints, e.g., matroids or paths in graphs. We first show that constant-factor approximation is NP-hard even in some special cases of matroids or paths. We then propose a polynomial-time algorithm for general matroids by assuming the number of states of nature to be a constant. We finally consider a relaxed notion of persuasiveness, called CCE-persuasiveness, and present a sufficient condition for polynomial-time approximability.
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