Private Bayesian Persuasion
Private Bayesian Persuasion
复制标题
私人贝叶斯说服
DOI：
10.2139/ssrn.2721307
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Y. Babichenko
中科院分区：
文献类型：
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作者：
Itai Arieli;Y. Babichenko
我们考虑一个多接收者贝叶斯说服问题，一个知情的发送者试图说服一组接收者采用某种产品。允许发送方承诺一个信令策略，在该策略中，发送方向每个接收方发送一个私有信号。发送者的效用是采纳者子集和实现状态的函数。我们首先考虑一个设置与二进制状态空间和接收器之间没有回报的外部性。我们刻画了两种不同类型的效用函数的最优信令策略和发送方的最大收益：超模和匿名次模。特别是，对于超级模块化公用事业，我们表明最优政策与尽可能采用该产品的积极建议相关。我们将这些结果推广到非二进制状态空间的情况。超模效用的结果被推广到接收者具有支付外部性的情况。我们还提供了一个充分必要条件下，公共和条件独立的信令策略是最优的。
We consider a multi-receiver Bayesian persuasion problem where an informed sender tries to persuade a group of receivers to adopt a certain product. The sender is allowed to commit to a signaling policy where she sends a private signal to every receiver. The utility of the sender is a function of the subset of adopters and the realized state. We first consider a setting with a binary state space and no payoff externalities among receivers. We characterize an optimal signaling policy and the maximal revenue to the sender for two different types of utility functions: supermodular, and anonymous submodular. In particular, for supermodular utilities we show that the optimal policy correlates positive recommendation to adopt the product as much as possible. We generalize these results to the case of a nonbinary state space. The result for supermodular utilities is generalized to the case where receivers have payoff externalities. We also provide a necessary and sufficient condition under which public and conditionally independent signaling policies are optimal.