# Mechanisms for a No-Regret Agent: Beyond the Common Prior

arXiv: https://arxiv.org/abs/2009.05518 · HTML: https://mlsanity.com/paper/2009.05518/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Sep 2020.

## Built on by (most cited first, 18 of 18)

- [Fast swap regret minimization and applications to approximate correlated equilibria](https://mlsanity.com/paper/2310.19647/) (2023)
- [Calibrated Stackelberg Games: Learning Optimal Commitments Against Calibrated Agents](https://mlsanity.com/paper/2306.02704/) (2023)
- [Contracting with a Learning Agent](https://mlsanity.com/paper/2401.16198/) (2024)
- [Full Swap Regret and Discretized Calibration](https://mlsanity.com/paper/2502.09332/) (2025)
- [Tractable Agreement Protocols](https://mlsanity.com/paper/2411.19791/) (2024)
- [Learning to Persuade on the Fly: Robustness Against Ignorance](https://mlsanity.com/paper/2102.10156/) (2021)
- [Swap Regret and Correlated Equilibria Beyond Normal-Form Games](https://mlsanity.com/paper/2502.20229/) (2025)
- [Persuading a Behavioral Agent: Approximately Best Responding and Learning](https://mlsanity.com/paper/2302.03719/) (2023)
- [Learning to Incentivize Information Acquisition: Proper Scoring Rules Meet Principal-Agent Model](https://mlsanity.com/paper/2303.08613/) (2023)
- [Generalized Principal-Agent Problem with a Learning Agent](https://mlsanity.com/paper/2402.09721/) (2024)
- [Is Knowledge Power? On the (Im)possibility of Learning from Strategic Interactions](https://mlsanity.com/paper/2408.08272/) (2024)
- [Repeated Contracting with Multiple Non-Myopic Agents: Policy Regret and Limited Liability](https://mlsanity.com/paper/2402.17108/) (2024)
- [Information Design with Unknown Prior](https://mlsanity.com/paper/2410.05533/) (2024)
- [Dimension-Free Decision Calibration for Nonlinear Loss Functions](https://mlsanity.com/paper/2504.15615/) (2025)
- [Near-optimal Swap Regret Minimization for Convex Losses](https://mlsanity.com/paper/2602.08862/) (2026)
- [Steering No-Regret Agents in MFGs under Model Uncertainty](https://mlsanity.com/paper/2503.09309/) (2025)
- [Algorithmic Collusion and the Complexity of Information-Value-Free Equilibria](https://mlsanity.com/paper/2609.22757/) (2026)
- [Prior-Agnostic Incentive-Compatible Exploration](https://mlsanity.com/paper/2602.20465/) (2026)

## Abstract (arXiv)

A rich class of mechanism design problems can be understood as incomplete-information games between a principal who commits to a policy and an agent who responds, with payoffs determined by an unknown state of the world. Traditionally, these models require strong and often-impractical assumptions about beliefs (a common prior over the state). In this paper, we dispense with the common prior. Instead, we consider a repeated interaction where both the principal and the agent may learn over time from the state history. We reformulate mechanism design as a reinforcement learning problem and develop mechanisms that attain natural benchmarks without any assumptions on the state-generating process. Our results make use of novel behavioral assumptions for the agent -- centered around counterfactual internal regret -- that capture the spirit of rationality without relying on beliefs.