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Presented By: Department of Economics

Freemium Model for Information Provision

Igal Milchtaich, Bar-Ilan University

Igal Milchtaich Igal Milchtaich
Igal Milchtaich
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 in standard persuasion models, the information seller (IS) is not affected by actions taken by the information buyer (IB), and is concerned solely with maximizing the revenue from selling information to the IB. Offering some information for free may increase the IB’s willingness to pay for additional information. The information that the IB seeks is modeled as information about the state of the world. Initially, the IB only knows the prior distribution over possible state. 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 gain in utility from the posterior induced by the free signal to the one 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 any revenue gain for the IS from providing free information is accompanied by an equally large or larger direct loss to the IB, implying that free information is never socially beneficial. Whether or not free information can increase the IS’s revenue depends on the form of the IB’s utility function. In the two-state case, the utility functions that allow such gains are 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, for example, when the IB uses the information to solve a decision problem. By contrast, when the IB is engaged in strategic interaction with a third party, the IS may benefit from providing free information. The paper presents a game‑theoretic example illustrating this possibility.
Igal Milchtaich Igal Milchtaich
Igal Milchtaich

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