# Algorithmic Bayesian Persuasion

arXiv: https://arxiv.org/abs/1503.05988 · HTML: https://mlsanity.com/paper/1503.05988/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Mar 2015.

## Built on by (most cited first, 21 of 21)

- [Sequential Information Design: Markov Persuasion Process and Its Efficient Reinforcement Learning](https://mlsanity.com/paper/2202.10678/) (2022)
- [Bayesian Persuasion for Algorithmic Recourse](https://mlsanity.com/paper/2112.06283/) (2021)
- [Must Read: A Comprehensive Survey of Computational Persuasion](https://mlsanity.com/paper/2505.07775/) (2025)
- [Learning to Persuade on the Fly: Robustness Against Ignorance](https://mlsanity.com/paper/2102.10156/) (2021)
- [Multi-Receiver Online Bayesian Persuasion](https://mlsanity.com/paper/2106.06480/) (2021)
- [Deep Contract Design via Discontinuous Networks](https://mlsanity.com/paper/2307.02318/) (2023)
- [Towards Strategic Persuasion with Language Models](https://mlsanity.com/paper/2509.22989/) (2025)
- [Multi-Sender Persuasion: A Computational Perspective](https://mlsanity.com/paper/2402.04971/) (2024)
- [Data Market Design through Deep Learning](https://mlsanity.com/paper/2310.20096/) (2023)
- [Markov Persuasion Processes: Learning to Persuade from Scratch](https://mlsanity.com/paper/2402.03077/) (2024)
- [Persuading a Behavioral Agent: Approximately Best Responding and Learning](https://mlsanity.com/paper/2302.03719/) (2023)
- [Information Design with Unknown Prior](https://mlsanity.com/paper/2410.05533/) (2024)
- [How to Sell High-Dimensional Data Optimally](https://mlsanity.com/paper/2510.15214/) (2025)
- [Algorithmic Collusion and the Complexity of Information-Value-Free Equilibria](https://mlsanity.com/paper/2609.22757/) (2026)
- [Algorithmic Information Design in Multi-Player Games: Possibility and Limits in Singleton Congestion](https://mlsanity.com/paper/2109.12445/) (2021)
- [Information Bargaining: Bilateral Commitment in Bayesian Persuasion](https://mlsanity.com/paper/2506.05876/) (2025)
- [Semantic Rate Distortion and Posterior Design: Compute Constraints, Multimodality, and Strategic Inference](https://mlsanity.com/paper/2602.03949/) (2026)
- [Meta-Learning for Repeated Bayesian Persuasion](https://mlsanity.com/paper/2603.20408/) (2026)
- [Algorithmic Feature Highlighting for Human-AI Decision-Making](https://mlsanity.com/paper/2604.22236/) (2026)
- [Structured Reinforcement Learning for Bayesian Persuasion : Application to Intelligent Interactive Driving](https://mlsanity.com/paper/2607.13576/) (2026)
- [On Incentivized Exploration beyond Bayesianism and Full-Information](https://mlsanity.com/paper/2607.18300/) (2026)

## Abstract (arXiv)

Persuasion, defined as the act of exploiting an informational advantage in order to effect the decisions of others, is ubiquitous. Indeed, persuasive communication has been estimated to account for almost a third of all economic activity in the US. This paper examines persuasion through a computational lens, focusing on what is perhaps the most basic and fundamental model in this space: the celebrated Bayesian persuasion model of Kamenica and Gentzkow. Here there are two players, a sender and a receiver. The receiver must take one of a number of actions with a-priori unknown payoff, and the sender has access to additional information regarding the payoffs. The sender can commit to revealing a noisy signal regarding the realization of the payoffs of various actions, and would like to do so as to maximize her own payoff assuming a perfectly rational receiver. We examine the sender's optimization task in three of the most natural input models for this problem, and essentially pin down its computational complexity in each. When the payoff distributions of the different actions are i.i.d. and given explicitly, we exhibit a polynomial-time (exact) algorithm, and a "simple" (1-1/e)-approximation algorithm. Our optimal scheme for the i.i.d. setting involves an analogy to auction theory, and makes use of Border's characterization of the space of reduced-forms for single-item auctions. When action payoffs are independent but non-identical with marginal distributions given explicitly, we show that it is #P-hard to compute the optimal expected sender utility. Finally, we consider a general (possibly correlated) joint distribution of action payoffs presented by a black box sampling oracle, and exhibit a fully polynomial-time approximation scheme (FPTAS) with a bi-criteria guarantee. We show that this result is the best possible in the black-box model for information-theoretic reasons.