Optimal Advertising for Information Products (2002.10045v5)

Abstract: When selling information products, the seller can provide some free partial information to change people's valuations so that the overall revenue can possibly be increased. We study the general problem of advertising information products by revealing partial information. We consider buyers who are decision-makers. The outcomes of the decision problems depend on the state of the world that is unknown to the buyers. The buyers can make their own observations and thus can hold different personal beliefs about the state of the world. There is an information seller who has access to the state of the world. The seller can promote the information by revealing some partial information. We assume that the seller chooses a long-term advertising strategy and then commits to it. The seller's goal is to maximize the expected revenue. We study the problem in two settings. (1) The seller targets buyers of a certain type. In this case, finding the optimal advertising strategy is equivalent to finding the concave closure of a simple function. The function is a product of two quantities, the likelihood ratio and the cost of uncertainty. Based on this observation, we prove some properties of the optimal mechanism, which allow us to solve for the optimal mechanism by a finite-size convex program. The convex program will have a polynomial-size if the state of the world has a constant number of possible realizations or the buyers face a decision problem with a constant number of options. For the general problem, we prove that it is NP-hard to find the optimal mechanism. (2) When the seller faces buyers of different types and only knows the distribution of their types, we provide an approximation algorithm when it is not too hard to predict the possible type of buyers who will make the purchase. For the general problem, we prove that it is NP-hard to find a constant-factor approximation.

• The paper demonstrates that computing optimal advertising strategies is NP-hard, even for homogenous buyer models.
• The study employs finite-size convex programming for bounded settings and introduces an approximation algorithm for heterogeneous buyers.
• The findings extend Bayesian persuasion theory by linking partial information disclosure with practical pricing and signaling approaches.

Optimal Advertising for Information Products

The paper "Optimal Advertising for Information Products" by Shuran Zheng and Yiling Chen addresses the strategic problem of how information sellers can maximize revenue by revealing partial information to potential buyers. In particular, the research explores the mechanisms and complexities of optimizing such advertising strategies in scenarios where buyers can hold varying beliefs regarding the state of the world, which the seller knows precisely.

Problem Formulation

The paper focuses on decision-makers (buyers) purchasing information products, influenced by partial information disclosed by sellers. In this context, the buyers face decision problems contingent on an unknown state of the world, while the seller has full access to this state. The buyers can make observations and hence possess personal probabilistic beliefs about the state of the world. When exposed to partial information, these beliefs may change, affecting the buyers’ decisions on whether to buy the complete information, thus impacting the seller’s revenue.

Key Contributions and Results

The authors investigate the advertising strategy under two distinct settings:

1. Single Buyer Type: When catering to a homogenous group of buyers who share the same probabilistic belief, the optimization of the advertising strategy involves computing the concave closure of a function resulting from the product of the likelihood ratio and the buyer’s cost of uncertainty (the expected value of knowing the true state). They prove that determining the optimal mechanism is NP-hard in general, though it can be efficiently computed when the state space or the decision space is bounded. The paper provides a finite-size convex programming solution and demonstrates the properties of the optimal mechanism, including the reduction of potential states visible to the buyer after seeing the partial information.
2. Multiple Buyer Types: When facing a heterogeneous mix of buyers with different belief distributions, the problem complicates as it now involves producing a pricing and signaling mechanism adaptable to varied buyer types. The paper introduces an approximation algorithm that can find an $\varepsilon$-suboptimal solution for the advertising mechanism when the likely buyers making a purchase can be anticipated with reasonable accuracy. They establish that achieving a precise, optimal solution remains NP-hard, even for a constant-factor approximation.

Implications and Future Directions

The research underscores the complexity inherent in designing optimal advertising strategies for information products, particularly under real-world conditions where buyers may hold different personal beliefs. From a theoretical standpoint, the findings enhance our understanding of Bayesian persuasion in the field of information economics. Practically, the methodologies proposed can be vital for industries heavily reliant on information sales, such as financial services, media, and data consultancy sectors, where strategic information revelation can significantly affect revenues.

Future research avenues could explore:

• Approximation Algorithms: Given the computational hardness of the problem, more robust and efficient approximation algorithms could be developed to handle larger and more complex state spaces.
• Dynamic Advertising Costs: Incorporating dynamic costs for revealing partial information would reflect more realistic scenarios where advertising incurs varying expenses.
• Interacting Multiple Rounds: Extending the model to scenarios where sellers can interact with buyers in multiple rounds, potentially employing sophisticated negotiation tactics or dynamic pricing models.
• Behavioral Economics: Integrating behavioral economics to account for irrational decision-making and its impact on the perceived value of information could refine the advertising strategies further.

In conclusion, this paper offers a comprehensive theoretical framework for optimizing information product advertising, revealing profound insights into the interplay between partial information disclosure and revenue maximization. The results are pivotal not only for academia but also for practical applications across various information-centric industries.