Einblick - Scientific Computing - # Bayesian Persuasion

Costly Bayesian Persuasion with a Partially Informed Sender: How the Cost of Information Affects Persuasion

Q: How might the dynamics of persuasion change in a setting with multiple receivers with varying levels of influence?

Introducing multiple receivers with varying levels of influence significantly complicates the dynamics of persuasion, pushing the model beyond its current binary sender-receiver framework. Here's how: Audience Heterogeneity: Receivers may have different prior beliefs (µ) and risk tolerances, leading to varying thresholds for persuasion (¯β). The sender would need to tailor their experiment (π) to target the most influential receivers or find a balance to persuade a sufficient coalition. Strategic Interactions: Receivers might observe each other's actions or communicate, leading to information cascades or herding behavior. A receiver's decision might be influenced by the perceived actions of others, even if it contradicts their own private information. Reputation and Signaling: The sender's reputation for trustworthiness and the accuracy of past experiments would play a crucial role. Receivers with higher influence might be less susceptible to persuasion attempts from senders with a history of biased information. Coalition Formation: The sender might try to build a coalition of receivers by strategically providing information that benefits some while potentially harming others. This could involve side deals or targeted information disclosure to exploit differences in receiver preferences. Cost Allocation: The cost of the experiment (c(π|µ)) might be shared among multiple receivers, introducing a public goods problem. Receivers with higher influence might be able to free-ride on the information paid for by others. Analyzing these dynamics would likely require tools from game theory, particularly those dealing with incomplete information and strategic communication, such as signaling games with multiple audiences or network games with information diffusion.

Q: Could the sender strategically manipulate the cost of information to their advantage, and if so, how would this affect the receiver's trust and decision-making?

Yes, the sender could potentially manipulate the cost of information to their advantage, but this would likely have significant consequences for the receiver's trust and decision-making: Inflated Costs: The sender could artificially inflate the cost of obtaining good news (Cg) to justify less informative experiments. This could mislead the receiver into believing that the sender is more confident than they actually are, especially if the receiver cannot independently verify the costs. Hidden Information: The sender might conduct parts of the experiment privately, selectively revealing only the favorable results while attributing the lack of negative information to high costs. This could create a biased sample and lead the receiver to make suboptimal decisions. Strategic Delay: The sender could strategically delay the release of information, citing unforeseen costs or complexities, to manage the receiver's expectations or wait for a more opportune moment to disclose the results. Such manipulations, if detected, would severely erode the receiver's trust in the sender. The receiver might become more skeptical of future persuasion attempts, demanding more transparency, independent verification of costs, or even resorting to acquiring information through their own channels. This could lead to: Increased Monitoring Costs: The receiver might invest more in monitoring the sender's actions, verifying information, or seeking second opinions, increasing the overall cost of decision-making. Reduced Information Sharing: The sender, anticipating the receiver's distrust, might be discouraged from conducting informative experiments in the first place, leading to a less efficient information environment. Adversarial Relationships: The relationship between the sender and receiver could become more adversarial, characterized by suspicion and a lack of cooperation, ultimately harming both parties.

Kernkonzepte

In Bayesian persuasion scenarios where information acquisition is costly, the sender's ability to persuade is contingent on the relative costs of acquiring positive versus negative information.

Zusammenfassung

Bibliographic Information: Jiang, S. (2024). Costly Persuasion by a Partially Informed Sender. arXiv preprint arXiv:2401.14087v4.
Research Objective: This paper investigates the dynamics of Bayesian persuasion when the sender possesses private information and incurs costs for conducting experiments to persuade the receiver. The research aims to understand how the cost structure of information acquisition influences the sender's strategies and the overall informativeness of the interaction.
Methodology: The study employs a game-theoretic model of Bayesian persuasion with a partially informed sender. The sender's cost of conducting an experiment is modeled as the expected reduction in a weighted log-likelihood ratio function, which is microfounded through a Wald sequential sampling problem. The analysis focuses on equilibria satisfying the D1 criterion.
Key Findings: The research reveals that the equilibrium outcome is highly sensitive to the relative costs of obtaining good news versus bad news. When good news is relatively inexpensive, a unique separating equilibrium emerges, where the sender's choice of experiment reveals their private information, leading to a more informed receiver compared to scenarios with an uninformed sender. However, when good news is significantly costlier, the single-crossing property, commonly observed in signaling games, ceases to hold. This results in the possibility of pooling and partial pooling equilibria, where the receiver may end up less informed compared to interactions with an uninformed sender.
Main Conclusions: The study challenges the intuitive notion that more informed senders always lead to more informative interactions. The cost of information plays a crucial role, and when acquiring good news is disproportionately expensive, it can disincentivize senders with favorable private information from conducting revealing experiments. This highlights the complex interplay between private information, information costs, and persuasion effectiveness.
Significance: This research contributes to the understanding of strategic information transmission in settings with costly information acquisition. It has implications for various fields, including economics, political science, and computer science, where persuasion and information design are central.
Limitations and Future Research: The study primarily focuses on binary state and action spaces. Future research could explore more general settings with multiple states, actions, or a wider range of cost functions. Additionally, investigating the robustness of the findings to alternative equilibrium refinements could provide further insights.

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Costly Persuasion by a Partially Informed Sender

by Shaofei Jian... um arxiv.org 11-19-2024

https://arxiv.org/pdf/2401.14087.pdf

Costly Persuasion by a Partially Informed Sender

Tiefere Fragen

How might the dynamics of persuasion change in a setting with multiple receivers with varying levels of influence?

Introducing multiple receivers with varying levels of influence significantly complicates the dynamics of persuasion, pushing the model beyond its current binary sender-receiver framework. Here's how:

Audience Heterogeneity:  Receivers may have different prior beliefs (µ) and risk tolerances, leading to varying thresholds for persuasion (¯β). The sender would need to tailor their experiment (π) to target the most influential receivers or find a balance to persuade a sufficient coalition.
Strategic Interactions: Receivers might observe each other's actions or communicate, leading to information cascades or herding behavior. A receiver's decision might be influenced by the perceived actions of others, even if it contradicts their own private information.
Reputation and Signaling: The sender's reputation for trustworthiness and the accuracy of past experiments would play a crucial role.  Receivers with higher influence might be less susceptible to persuasion attempts from senders with a history of biased information.
Coalition Formation: The sender might try to build a coalition of receivers by strategically providing information that benefits some while potentially harming others. This could involve side deals or targeted information disclosure to exploit differences in receiver preferences.
Cost Allocation: The cost of the experiment (c(π|µ)) might be shared among multiple receivers, introducing a public goods problem. Receivers with higher influence might be able to free-ride on the information paid for by others.
Analyzing these dynamics would likely require tools from game theory, particularly those dealing with incomplete information and strategic communication, such as signaling games with multiple audiences or network games with information diffusion.

Could the sender strategically manipulate the cost of information to their advantage, and if so, how would this affect the receiver's trust and decision-making?

Yes, the sender could potentially manipulate the cost of information to their advantage, but this would likely have significant consequences for the receiver's trust and decision-making:

Inflated Costs: The sender could artificially inflate the cost of obtaining good news (Cg) to justify less informative experiments. This could mislead the receiver into believing that the sender is more confident than they actually are, especially if the receiver cannot independently verify the costs.
Hidden Information: The sender might conduct parts of the experiment privately, selectively revealing only the favorable results while attributing the lack of negative information to high costs. This could create a biased sample and lead the receiver to make suboptimal decisions.
Strategic Delay: The sender could strategically delay the release of information, citing unforeseen costs or complexities, to manage the receiver's expectations or wait for a more opportune moment to disclose the results.
Such manipulations, if detected, would severely erode the receiver's trust in the sender. The receiver might become more skeptical of future persuasion attempts, demanding more transparency, independent verification of costs, or even resorting to acquiring information through their own channels. This could lead to:

Increased Monitoring Costs: The receiver might invest more in monitoring the sender's actions, verifying information, or seeking second opinions, increasing the overall cost of decision-making.
Reduced Information Sharing: The sender, anticipating the receiver's distrust, might be discouraged from conducting informative experiments in the first place, leading to a less efficient information environment.
Adversarial Relationships:  The relationship between the sender and receiver could become more adversarial, characterized by suspicion and a lack of cooperation, ultimately harming both parties.

What are the ethical implications of these findings, particularly in contexts like healthcare or public policy, where information asymmetry and persuasion can have significant consequences?

The findings presented in the paper raise significant ethical concerns, especially in fields like healthcare and public policy, where information asymmetry is prevalent and persuasion can have far-reaching consequences:

Patient Autonomy: In healthcare, if pharmaceutical companies strategically manipulate the cost and presentation of clinical trial data to favor their drugs, it could undermine informed consent and patient autonomy. Patients might make decisions based on incomplete or biased information, potentially jeopardizing their health.
Policy Manipulation: In public policy, interest groups or lobbyists could exploit the cost of information to influence policymakers' decisions. By selectively funding studies or presenting data in a misleading way, they could promote policies that serve their interests at the expense of the public good.
Transparency and Accountability: The potential for manipulation highlights the need for greater transparency and accountability in how information is generated, analyzed, and disseminated. Independent verification of research findings, open access to data, and clear disclosure of funding sources are crucial to ensure ethical conduct.
Trust in Experts:  The erosion of trust in experts is a significant concern. If the public loses faith in the integrity of scientific research or the objectivity of policy analysis, it can lead to skepticism towards evidence-based decision-making and hinder progress in addressing critical societal challenges.
Addressing these ethical implications requires a multi-faceted approach:

Regulation and Oversight:  Stronger regulations and oversight mechanisms are needed to prevent the manipulation of information, particularly in sectors with significant information asymmetry.
Ethical Guidelines:  Professional organizations and research institutions should establish and enforce ethical guidelines for conducting and communicating research, emphasizing transparency, objectivity, and the responsible use of data.
Media Literacy:  Promoting media literacy and critical thinking skills among the public is essential to empower individuals to evaluate information sources, identify potential biases, and make informed decisions.
Open Science Practices: Encouraging open science practices, such as data sharing and pre-registration of studies, can increase transparency and allow for independent scrutiny of research findings.
By acknowledging and addressing these ethical implications, we can strive to create a more informed and just society where persuasion is based on credible evidence and serves the best interests of all stakeholders.