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Reputation-based Persuasion Platforms

Itai Arieli, Omer Madmon, Moshe Tennenholtz

TL;DR

The paper studies a bi-level Bayesian persuasion problem in which a third-party platform controls the sender’s information about users, with the platform aiming to maximize average user welfare. In the one-shot setting, the problem is shown to be strategically equivalent to Bergemann et al.'s market segmentation, allowing efficient computation via their algorithm by mapping persuasion thresholds to valuations through $V=igrace{ u_{ heta}=oldsymbol{eta}+(1-oldsymbol{eta}) au_{ heta}igrace}$ and $oldsymbol{\\pi}=x^*$, with the pricing rule $oldsymbol{\\phi}(oldsymbol{\\pi})=oldsymbol{eta}+(1-oldsymbol{\\beta})p(x)$. A reputation-based extension introduces sequential arrivals and a punishment mechanism that moves the sender to a low-reputation state if truthful signaling is violated; in this setting the optimal policy can be characterized by a two-step procedure that applies Bergemann’s algorithm to the part of the posterior where truthful signaling is not enforced, after solving a finite-dimensional optimization involving $(oldsymbol{\\alpha}, x^T, x^F)$. The results reveal that, under suitable conditions, the reputation mechanism can enhance welfare while maintaining incentive compatibility, with numerical evidence suggesting the platform’s strategy may privilege users who are harder to persuade, especially when the sender is less patient. Overall, the paper contributes a novel two-level information-design framework, a tractable reduction to market segmentation for the one-shot case, and a principled characterization of optimal, reputation-based platform policies, with extensions to richer state spaces and practical implications for reputation-enabled platforms.

Abstract

In this paper, we introduce a two-stage Bayesian persuasion model in which a third-party platform controls the information available to the sender about users' preferences. We aim to characterize the optimal information disclosure policy of the platform, which maximizes average user utility, under the assumption that the sender also follows its own optimal policy. We show that this problem can be reduced to a model of market segmentation, in which probabilities are mapped into valuations. We then introduce a repeated variation of the persuasion platform problem in which myopic users arrive sequentially. In this setting, the platform controls the sender's information about users and maintains a reputation for the sender, punishing it if it fails to act truthfully on a certain subset of signals. We provide a characterization of the optimal platform policy in the reputation-based setting, which is then used to simplify the optimization problem of the platform.

Reputation-based Persuasion Platforms

TL;DR

The paper studies a bi-level Bayesian persuasion problem in which a third-party platform controls the sender’s information about users, with the platform aiming to maximize average user welfare. In the one-shot setting, the problem is shown to be strategically equivalent to Bergemann et al.'s market segmentation, allowing efficient computation via their algorithm by mapping persuasion thresholds to valuations through and , with the pricing rule . A reputation-based extension introduces sequential arrivals and a punishment mechanism that moves the sender to a low-reputation state if truthful signaling is violated; in this setting the optimal policy can be characterized by a two-step procedure that applies Bergemann’s algorithm to the part of the posterior where truthful signaling is not enforced, after solving a finite-dimensional optimization involving . The results reveal that, under suitable conditions, the reputation mechanism can enhance welfare while maintaining incentive compatibility, with numerical evidence suggesting the platform’s strategy may privilege users who are harder to persuade, especially when the sender is less patient. Overall, the paper contributes a novel two-level information-design framework, a tractable reduction to market segmentation for the one-shot case, and a principled characterization of optimal, reputation-based platform policies, with extensions to richer state spaces and practical implications for reputation-enabled platforms.

Abstract

In this paper, we introduce a two-stage Bayesian persuasion model in which a third-party platform controls the information available to the sender about users' preferences. We aim to characterize the optimal information disclosure policy of the platform, which maximizes average user utility, under the assumption that the sender also follows its own optimal policy. We show that this problem can be reduced to a model of market segmentation, in which probabilities are mapped into valuations. We then introduce a repeated variation of the persuasion platform problem in which myopic users arrive sequentially. In this setting, the platform controls the sender's information about users and maintains a reputation for the sender, punishing it if it fails to act truthfully on a certain subset of signals. We provide a characterization of the optimal platform policy in the reputation-based setting, which is then used to simplify the optimization problem of the platform.
Paper Structure (31 sections, 18 theorems, 48 equations, 4 figures)

This paper contains 31 sections, 18 theorems, 48 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Persuasion platforms
  3. Reputation-based persuasion platforms
  4. Our contribution
  5. Paper structure
  6. Related Work
  7. Persuasion Platforms
  8. The Model
  9. Market Segmentation
  10. Optimal Platform Policy: From Probabilities To Valuations
  11. Achieving the Pareto-frontier
  12. Beyond Binary State Space
  13. Multiple states with a single global low-quality state
  14. Continuous state space
  15. Reputation-based Persuasion Platforms
  16. ...and 16 more sections

Key Result

Theorem 1

Given a persuasion platform problem instance $(\Theta, x^*, \mu)$, consider the equivalent market segmentation problem $(V, \pi^*)$. For any user distribution $x$ (and its corresponding market $\pi$) and for any sender policy $p$ (and its corresponding pricing rule $\phi$) the following properties h

Figures (4)

  • Figure 1: The interaction between the Platform, the Sender, and the User.
  • Figure 2: The feasible surplus triangle. bergemann2015 provide an algorithm for finding a consumer surplus maximizing segmentation $\sigma^*$ for a given market $\pi^*$ (point B).
  • Figure 3: Reputation-based Persuasion Platform as an MDP for the sender.
  • Figure 4: Utility of the sender and truthful posterior as functions of $\delta$ for different priors. Each row represents a different prior (30%, 50%, and 70%), with the left column showing the sender's utility and the right column displaying the truthful posterior.

Theorems & Definitions (35)

  • Definition 1
  • Theorem 1
  • proof
  • Corollary 1
  • Corollary 2
  • Corollary 3
  • Theorem 2
  • Proposition 1
  • proof
  • Definition 2
  • ...and 25 more