信息提供的免费增值模式

中文摘要 AI 辅助

本文研究用于信息销售的理论免费增值模型，借鉴了重复零和博弈与贝叶斯说服研究中使用的数学工具。与标准贝叶斯说服模型不同，信息卖方（IS）对信息买方（IB）采取的行动持中立态度，仅关注最大化信息销售的收入。提供部分免费信息可能会提高IB为额外信息付费的意愿。IB寻求的信息是关于世界状态的，初始时IB仅知道可能状态的先验分布，IS通过信号提供免费和付费信息，这些信号的状态依赖分布通过贝叶斯规则确定IB的后验分布，IB的效用是后验的函数。最优免费信号是能最大化IS从后续付费信号中获得的预期收入的信号，该收入等于IB从免费信号诱导的后验转移到付费信号诱导的后验时的预期效用增益。本文刻画了最优免费和付费信号，并根据IB的效用函数推导了最大收入的公式，表明IS从提供免费信息中获得的收入增益伴随着IB的损失，免费信息能否增加IS的收入取决于IB效用函数的形式：在两状态情况下，这种依赖关系得到完全刻画；在一般情况下，仅得到必要条件，特别是若IB的效用函数是凸的，IS永远无法从提供免费信息中获利，当IB使用信息解决决策问题时就会出现这种情况，相比之下，当IB与第三方进行策略互动时，IS可能会从提供免费信息中获益。

英文摘要

The paper explores a theoretical freemium model for the sale of information, drawing on mathematical tools used in the study of repeated zero-sum games and Bayesian persuasion. Unlike standard Bayesian persuasion models, the information seller (IS) is indifferent to the actions taken by the information buyer (IB) and is concerned solely with maximizing the revenue from selling information. Offering some information for free may increase the IB's willingness to pay for additional information. The information that the IB seeks is about the state of the world. Initially, the IB only knows the prior distribution over possible states. The IS supplies both free and paid information through signals whose state-dependent distributions determine the IB's posterior via Bayes' rule. The IB's utility is a function of the posterior. An optimal free signal is one that maximizes the IS's expected revenue from the subsequent paid signal. That revenue is equal to the IB's expected utility gain when moving from the posterior induced by the free signal to that induced by the paid signal. The paper characterizes the optimal free and paid signals and derives a formula for the maximal revenue in terms of the IB's utility function. It shows that a revenue gain for the IS from the provision of free information is accompanied by a loss to the IB. Whether free information can increase the IS's revenue depends on the form of the IB's utility function. In the two-state case, that dependence is fully characterized. In the general case, only necessary conditions are obtained. In particular, if the IB's utility function is convex, the IS can never profit from providing free information. This occurs, in particular, when the IB uses the information to solve a decision problem. By contrast, when the IB is engaged in a strategic interaction with a third party, the IS may benefit from providing free information.

发表机构

• Bar-Ilan University（巴伊兰大学）

机构由 AI 辅助整理，请以论文原文为准。