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https://doi.org/10.2139/ssrn.4...
Article . 2024 . Peer-reviewed
Data sources: Crossref
https://dx.doi.org/10.48550/ar...
Article . 2024
License: CC BY
Data sources: Datacite
DBLP
Preprint . 2024
Data sources: DBLP
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Informativeness and Trust in Bayesian Persuasion

Authors: Reema Deori; Ankur A. Kulkarni;

Informativeness and Trust in Bayesian Persuasion

Abstract

A persuasion policy successfully persuades an agent to pick a particular action only if the information is designed in a manner that convinces the agent that it is in their best interest to pick that action. Thus, it is natural to ask, what makes the agent trust the persuader's suggestion? We study a Bayesian persuasion interaction between a sender and a receiver where the sender has access to private information and the receiver attempts to recover this information from messages sent by the sender. The sender crafts these messages in an attempt to maximize its utility which depends on the source symbol and the symbol recovered by the receiver. Our goal is to characterize the \textit{Stackelberg game value}, and the amount of true information revealed by the sender during persuasion. We find that the SGV is given by the optimal value of a \textit{linear program} on probability distributions constrained by certain \textit{trust constraints}. These constraints encode that any signal in a persuasion strategy must contain more truth than untruth and thus impose a fundamental bound on the extent of obfuscation a sender can perform. We define \textit{informativeness} of the sender as the minimum expected number of symbols truthfully revealed by the sender in any accumulation point of a sequence of $\varepsilon$-equilibrium persuasion strategies, and show that it is given by another linear program. Informativeness is a fundamental bound on the amount of information the sender must reveal to persuade a receiver. Closed form expressions for the SGV and the informativeness are presented for structured utility functions. This work generalizes our previous work where the sender and the receiver were constrained to play only deterministic strategies and a similar notion of informativeness was characterized. Comparisons between the previous and current notions are discussed.

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Keywords

FOS: Computer and information sciences, FOS: Economics and business, Computer Science - Computer Science and Game Theory, Economics - Theoretical Economics, FOS: Electrical engineering, electronic engineering, information engineering, Theoretical Economics (econ.TH), Systems and Control (eess.SY), Electrical Engineering and Systems Science - Systems and Control, 91A28, 91A65, Computer Science and Game Theory (cs.GT)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green