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Bayesian Persuasion with Externalities: Exploiting Agent Types
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Studies optimal signaling for Bayesian persuasion of multiple agents with externalities and agent types under public, private, and semi-private channels, giving revelation-principle characterizations and LP-based polynomial algorithms when joint deviations are bounded by a constant.
Problem
Computing optimal signaling policies for a principal persuading multiple agents whose utilities have externalities (joint deviations), under public, private, and semi-private signaling channels.
Approach
Shows the classical revelation principle fails with joint deviations and introduces representative action vectors, blocking profiles (signatures) and lottery policies, using agent types to build polynomial-size LPs when the deviation size is constant and proving NP-hardness otherwise.
Key results
- Public, semi-private and private persuasion admit polynomial-time LP-based algorithms for optimal policies when the maximum number of deviating agents d, number of types, and number of actions are constants.
- When d is part of the input, computing optimal public, semi-private, or private policies is NP-hard (reduction from Vertex Cover).
- Revelation principle in its classical form fails with joint deviations; a 3-action two-agent example shows recommending only actions is suboptimal, motivating blocking-profile characterizations.
Surprising findings
- Private persuasion can achieve strictly higher principal utility than semi-private and public persuasion, since representative action vectors are not without loss of optimality in the private case.
Limitations
- Polynomial-time results require constant deviation bound d, number of types and actions.
- Assumes non-transferable utility and no further communication among agents.
- Types are assumed known to the principal in advance.
Experimental setup
Builds on: Bayesian persuasion revelation principle Hall's theorem
Closest papers by meaning
- Computational Aspects of Bayesian Persuasion under Approximate Best Response (NeurIPS 2024 · similarity 0.90)
- Online Bayesian Persuasion Without a Clue (NeurIPS 2024 · similarity 0.89)
- Multi-Sender Persuasion: A Computational Perspective (ICML 2024 · similarity 0.89)
- Markov Persuasion Processes: Learning to Persuade From Scratch (NeurIPS 2025 · similarity 0.87)
- Persuasive Prediction via Decision Calibration (NeurIPS 2026 · similarity 0.86)
- Learning to Persuade a Biased Receiver (NeurIPS 2026 · similarity 0.85)
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