# Is Knowledge Power? On the (Im)possibility of Learning from Strategic Interactions

arXiv: https://arxiv.org/abs/2408.08272 · HTML: https://mlsanity.com/paper/2408.08272/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 43 references that are in the map.
- First posted on arXiv 15 Aug 2024.

## Builds on (most cited first, 28 of 28)

- [Who Leads and Who Follows in Strategic Classification?](https://mlsanity.com/paper/2106.12529/) (2021)
- [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)
- [Learning Prices for Repeated Auctions with Strategic Buyers](https://mlsanity.com/paper/1311.6838/) (2013)
- [Strategizing against Learners in Bayesian Games](https://mlsanity.com/paper/2205.08562/) (2022)
- [Fast swap regret minimization and applications to approximate correlated equilibria](https://mlsanity.com/paper/2310.19647/) (2023)
- [Learning in Stackelberg Games with Non-myopic Agents](https://mlsanity.com/paper/2208.09407/) (2022)
- [Convergence of Learning Dynamics in Stackelberg Games](https://mlsanity.com/paper/1906.01217/) (2019)
- [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)
- [Is Learning in Games Good for the Learners?](https://mlsanity.com/paper/2305.19496/) (2023)
- [Mechanisms for a No-Regret Agent: Beyond the Common Prior](https://mlsanity.com/paper/2009.05518/) (2020)
- [Watch and Learn: Optimizing from Revealed Preferences Feedback](https://mlsanity.com/paper/1504.01033/) (2015)
- [How and Why to Manipulate Your Own Agent: On the Incentives of Users of Learning Agents](https://mlsanity.com/paper/2112.07640/) (2021)
- [Pareto-Optimal Algorithms for Learning in Games](https://mlsanity.com/paper/2402.09549/) (2024)
- [Online Learning in Stackelberg Games with an Omniscient Follower](https://mlsanity.com/paper/2301.11518/) (2023)
- [Optimally Deceiving a Learning Leader in Stackelberg Games](https://mlsanity.com/paper/2006.06566/) (2020)
- [From External to Swap Regret 2.0: An Efficient Reduction and Oblivious Adversary for Large Action Spaces](https://mlsanity.com/paper/2310.19786/) (2023)
- [Efficient Prior-Free Mechanisms for No-Regret Agents](https://mlsanity.com/paper/2311.07754/) (2023)
- [Imitative Follower Deception in Stackelberg Games](https://mlsanity.com/paper/1903.02917/) (2019)
- [Efficient Stackelberg Strategies for Finitely Repeated Games](https://mlsanity.com/paper/2207.04192/) (2022)
- [Manipulating a Learning Defender and Ways to Counteract](https://mlsanity.com/paper/1905.11759/) (2019)
- [Strategizing against No-Regret Learners in First-Price Auctions](https://mlsanity.com/paper/2402.08637/) (2024)
- [Robust No-Regret Learning in Min-Max Stackelberg Games](https://mlsanity.com/paper/2203.14126/) (2022)
- [Regret Analysis of Repeated Delegated Choice](https://mlsanity.com/paper/2310.04884/) (2023)
- [Impact of Decentralized Learning on Player Utilities in Stackelberg Games](https://mlsanity.com/paper/2403.00188/) (2024)
- [Learning to Manipulate a Commitment Optimizer](https://mlsanity.com/paper/2302.11829/) (2023)
- [Optimal Private Payoff Manipulation against Commitment in Extensive-form Games](https://mlsanity.com/paper/2206.13119/) (2022)

## Built on by (most cited first, 5 of 5)

- [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)
- [From No-Regret to Strategically Robust Learning in Repeated Auctions](https://mlsanity.com/paper/2601.03853/) (2026)
- [Learning Local Stackelberg Equilibria from Repeated Interactions with a Learning Agent](https://mlsanity.com/paper/2510.22471/) (2025)

## Abstract (arXiv)

When learning in strategic environments, a key question is whether agents can overcome uncertainty about their preferences to achieve outcomes they could have achieved absent any uncertainty. Can they do this solely through interactions with each other? We focus this question on the ability of agents to attain the value of their Stackelberg optimal strategy and study the impact of information asymmetry. We study repeated interactions in fully strategic environments where players' actions are decided based on learning algorithms that take into account their observed histories and knowledge of the game. We study the pure Nash equilibria (PNE) of a meta-game where players choose these algorithms as their actions. We demonstrate that if one player has perfect knowledge about the game, then any initial informational gap persists. That is, while there is always a PNE in which the informed agent achieves her Stackelberg value, there is a game where no PNE of the meta-game allows the partially informed player to achieve her Stackelberg value. On the other hand, if both players start with some uncertainty about the game, the quality of information alone does not determine which agent can achieve her Stackelberg value. In this case, the concept of information asymmetry becomes nuanced and depends on the game's structure. Overall, our findings suggest that repeated strategic interactions alone cannot facilitate learning effectively enough to earn an uninformed player her Stackelberg value.