# Generalized Principal-Agent Problem with a Learning Agent

arXiv: https://arxiv.org/abs/2402.09721 · HTML: https://mlsanity.com/paper/2402.09721/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 59 references that are in the map.
- First posted on arXiv 15 Feb 2024.

## Builds on (most cited first, 22 of 22)

- [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)
- [Econometrics for Learning Agents](https://mlsanity.com/paper/1505.00720/) (2015)
- [Contracting with a Learning Agent](https://mlsanity.com/paper/2401.16198/) (2024)
- [Selling to Multiple No-Regret Buyers](https://mlsanity.com/paper/2307.04175/) (2023)
- [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)
- [Pareto-Optimal Algorithms for Learning in Games](https://mlsanity.com/paper/2402.09549/) (2024)
- [Learning to Persuade on the Fly: Robustness Against Ignorance](https://mlsanity.com/paper/2102.10156/) (2021)
- [Efficient Prior-Free Mechanisms for No-Regret Agents](https://mlsanity.com/paper/2311.07754/) (2023)
- [Information Design in Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2305.06807/) (2023)
- [Markov Persuasion Processes: Learning to Persuade from Scratch](https://mlsanity.com/paper/2402.03077/) (2024)
- [Strategizing against No-Regret Learners in First-Price Auctions](https://mlsanity.com/paper/2402.08637/) (2024)
- [Robust Stackelberg Equilibria](https://mlsanity.com/paper/2304.14990/) (2023)
- [Strategically-Robust Learning Algorithms for Bidding in First-Price Auctions](https://mlsanity.com/paper/2402.07363/) (2024)
- [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)
- [Generalized Principal-Agency: Contracts, Information, Games and Beyond](https://mlsanity.com/paper/2209.01146/) (2022)
- [No-Regret Bayesian Recommendation to Homogeneous Users](https://mlsanity.com/paper/2202.06135/) (2022)
- [Computational Aspects of Bayesian Persuasion under Approximate Best Response](https://mlsanity.com/paper/2402.07426/) (2024)
- [Persuading Risk-Conscious Agents: A Geometric Approach](https://mlsanity.com/paper/2208.03758/) (2022)

## Built on by (most cited first, 6 of 6)

- [Principal-Agent Bandit Games with Self-Interested and Exploratory Learning Agents](https://mlsanity.com/paper/2412.16318/) (2024)
- [From No-Regret to Strategically Robust Learning in Repeated Auctions](https://mlsanity.com/paper/2601.03853/) (2026)
- [Bayesian Decision Making around Experts](https://mlsanity.com/paper/2510.08113/) (2025)
- [Is Online Linear Optimization Sufficient for Strategic Robustness?](https://mlsanity.com/paper/2602.12253/) (2026)
- [No Coin Left Behind: Maximizing Strategic Surplus Against No-Regret Dynamics](https://mlsanity.com/paper/2604.05129/) (2026)
- [Mean-based algorithms: A lower bound and regret](https://mlsanity.com/paper/2606.04931/) (2026)

## Abstract (arXiv)

In classic principal-agent problems such as Stackelberg games, contract design, and Bayesian persuasion, the agent best responds to the principal's committed strategy. We study repeated generalized principal-agent problems under the assumption that the principal does not have commitment power and the agent uses algorithms to learn to respond to the principal. We reduce this problem to a one-shot problem where the agent approximately best responds, and prove that: (1) If the agent uses contextual no-regret learning algorithms with regret Reg(T), then the principal can guarantee utility at least U^* - Thetabig(√tfracReg(T)Tbig), where U^* is the principal's optimal utility in the classic model with a best-responding agent. (2) If the agent uses contextual no-swap-regret learning algorithms with swap-regret SReg(T), then the principal cannot obtain utility more than U^* + O(fracSReg(T)T). (3) In addition, if the agent uses mean-based learning algorithms (which can be no-regret but not no-swap-regret), then the principal can sometimes do significantly better than U^*. These results not only refine previous works on Stackelberg games and contract design, but also lead to new results for Bayesian persuasion with a learning agent and all generalized principal-agent problems where the agent does not have private information.