Optimizing Messaging Policies Through Simulation-Based Queries in Bayesian Persuasion

Kernekoncepter

The sender can improve their messaging policy by querying a simulation oracle that provides information about the receiver's optimal actions given different messaging policies. The sender's optimal querying policy can be computed efficiently using dynamic programming.

Resumé

The key insights and findings of the content are:

In a binary Bayesian persuasion setting, the sender's optimal messaging policy can be characterized as using at most two messages. One message has a threshold that separates receiver beliefs into those that take action 1 and those that take action 0. The other message can either induce all receivers to take action 1, no receivers to take action 1, or have a different threshold.

The sender can query a simulation oracle to gain information about the receiver's beliefs and improve their messaging policy. Each simulation query corresponds to a threshold that partitions the receiver beliefs.

The sender's optimal querying policy can be computed efficiently using dynamic programming. The algorithm first precomputes the optimal messaging policy for any range of receiver beliefs. It then iteratively builds the optimal querying policy by considering the value of each possible query given the optimal policies for smaller subsets of receiver beliefs.

The optimal querying policy can be implemented adaptively by binary searching over the set of queries identified by the dynamic program. This adaptive policy is as informative as the optimal non-adaptive policy using the same number of queries.

The results extend to settings with approximate oracles, more general query structures, and costly queries.

The content provides a principled approach for a sender to leverage simulation-based queries to optimize their messaging policy in a Bayesian persuasion setting with an informed receiver.

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Algorithmic Persuasion Through Simulation

by Keegan Harri... kl. arxiv.org 04-05-2024

https://arxiv.org/pdf/2311.18138.pdf

Dybere Forespørgsler

How would the results change if the state space and/or action space were not binary

In the case where the state space and/or action space are not binary, the results and implications of the model would change.

State Space: If the state space is not binary, the sender's optimal messaging policy may involve more than two messages. The complexity of determining the optimal messaging policy would increase as the number of potential states grows. The sender would need to consider a wider range of possible messages to effectively persuade the receiver. Additionally, the structure of the simulation queries and the optimal querying policy may need to be adapted to accommodate a non-binary state space.

Action Space: Similarly, if the action space is not binary, the sender's optimal messaging policy would need to account for multiple possible actions that the receiver could take. This would require a more nuanced approach to crafting persuasive messages that cater to different potential actions. The sender would need to optimize their messaging strategy to elicit the desired response from the receiver, considering the various actions available.

Overall, a non-binary state and/or action space would introduce additional complexity to the model, requiring more sophisticated strategies for optimal messaging and querying policies.

How might the sender's optimal querying and messaging policies change if the receiver also has a private type that impacts their utility, in addition to their private signal about the state

If the receiver also has a private type that impacts their utility in addition to their private signal about the state, the sender's optimal querying and messaging policies would need to be adjusted accordingly.

Optimal Querying Policy: The sender would need to consider not only the receiver's beliefs about the state but also their private type that influences their utility. This additional information would impact the sender's decision-making process when selecting queries to refine their understanding of the receiver. The optimal querying policy would need to take into account both the receiver's beliefs and their private type to effectively tailor the messaging strategy.

Optimal Messaging Policy: With the receiver's private type influencing their utility, the sender's optimal messaging policy would need to be designed to appeal to both the receiver's beliefs about the state and their private type. The messaging strategy would need to be crafted in a way that addresses the receiver's preferences and motivations based on their private type, in addition to their beliefs. This would require a more nuanced and personalized approach to persuasion.

Incorporating the receiver's private type into the model would enhance the sender's ability to tailor their messaging and querying strategies for more effective persuasion.

What are some potential real-world applications of this framework beyond the product marketing example, and how might the details of the model need to be adapted for those settings

The framework presented in the context of algorithmic persuasion through simulation has various real-world applications beyond product marketing. Some potential applications include:

Political Campaigns: Political campaigns could utilize this framework to tailor their messaging strategies to different voter segments based on their beliefs and preferences. By understanding the private types and signals of voters, political campaigns can optimize their communication to persuade individuals effectively.

Financial Services: In the financial services industry, this framework could be used to personalize messaging and offerings to clients based on their financial goals, risk tolerance, and other private types. By leveraging simulation queries and optimal messaging policies, financial institutions can enhance their client engagement and decision-making processes.

Healthcare Communication: Healthcare providers could apply this framework to improve patient communication and adherence to treatment plans. By understanding patients' beliefs, preferences, and private types, healthcare professionals can tailor their messaging to encourage positive health behaviors and outcomes.

Adapting the model for these settings would involve customizing the simulation queries, messaging policies, and querying strategies to suit the specific characteristics and objectives of each application domain. The details of the model would need to be adjusted to account for the unique dynamics and requirements of these real-world scenarios.