# Persuading a Behavioral Agent: Approximately Best Responding and Learning

arXiv: https://arxiv.org/abs/2302.03719 · HTML: https://mlsanity.com/paper/2302.03719/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 41 references that are in the map.
- First posted on arXiv 7 Feb 2023.

## Builds on (most cited first, 12 of 12)

- [Strategizing against No-regret Learners](https://mlsanity.com/paper/1909.13861/) (2019)
- [Selling to a No-Regret Buyer](https://mlsanity.com/paper/1711.09176/) (2017)
- [Strategizing against Learners in Bayesian Games](https://mlsanity.com/paper/2205.08562/) (2022)
- [Algorithmic Bayesian Persuasion](https://mlsanity.com/paper/1503.05988/) (2015)
- [Mechanisms for a No-Regret Agent: Beyond the Common Prior](https://mlsanity.com/paper/2009.05518/) (2020)
- [Sequential Information Design: Markov Persuasion Process and Its Efficient Reinforcement Learning](https://mlsanity.com/paper/2202.10678/) (2022)
- [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)
- [Rationality-Robust Information Design: Bayesian Persuasion under Quantal Response](https://mlsanity.com/paper/2207.08253/) (2022)
- [Regret-Minimizing Bayesian Persuasion](https://mlsanity.com/paper/2105.13870/) (2021)
- [No-Regret Bayesian Recommendation to Homogeneous Users](https://mlsanity.com/paper/2202.06135/) (2022)
- [Persuading Risk-Conscious Agents: A Geometric Approach](https://mlsanity.com/paper/2208.03758/) (2022)

## Built on by (most cited first, 7 of 7)

- [The Double-Edged Sword of Behavioral Responses in Strategic Classification: Theory and User Studies](https://mlsanity.com/paper/2410.18066/) (2024)
- [Maximizing utility in multi-agent environments by anticipating the behavior of other learners](https://mlsanity.com/paper/2407.04889/) (2024)
- [Strategically-Robust Learning Algorithms for Bidding in First-Price Auctions](https://mlsanity.com/paper/2402.07363/) (2024)
- [Learning to Play Against Unknown Opponents](https://mlsanity.com/paper/2412.18297/) (2024)
- [Best of Both Worlds: Regret Minimization versus Minimax Play](https://mlsanity.com/paper/2502.11673/) (2025)
- [Computational Intractability of Strategizing against Online Learners](https://mlsanity.com/paper/2503.04202/) (2025)
- [Structured Reinforcement Learning for Bayesian Persuasion : Application to Intelligent Interactive Driving](https://mlsanity.com/paper/2607.13576/) (2026)

## Abstract (arXiv)

The classic Bayesian persuasion model assumes a Bayesian and best-responding receiver. We study a relaxation of the Bayesian persuasion model where the receiver can approximately best respond to the sender's signaling scheme. We show that, under natural assumptions, (1) the sender can find a signaling scheme that guarantees itself an expected utility almost as good as its optimal utility in the classic model, no matter what approximately best-responding strategy the receiver uses; (2) on the other hand, there is no signaling scheme that gives the sender much more utility than its optimal utility in the classic model, even if the receiver uses the approximately best-responding strategy that is best for the sender. Together, (1) and (2) imply that the approximately best-responding behavior of the receiver does not affect the sender's maximal achievable utility a lot in the Bayesian persuasion problem. The proofs of both results rely on the idea of robustification of a Bayesian persuasion scheme: given a pair of the sender's signaling scheme and the receiver's strategy, we can construct another signaling scheme such that the receiver prefers to use that strategy in the new scheme more than in the original scheme, and the two schemes give the sender similar utilities. As an application of our main result (1), we show that, in a repeated Bayesian persuasion model where the receiver learns to respond to the sender by some algorithms, the sender can do almost as well as in the classic model. Interestingly, unlike (2), with a learning receiver the sender can sometimes do much better than in the classic model.