# Learning to Manipulate a Commitment Optimizer

arXiv: https://arxiv.org/abs/2302.11829 · HTML: https://mlsanity.com/paper/2302.11829/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 27 references that are in the map.
- First posted on arXiv 23 Feb 2023.

## Builds on (most cited first, 11 of 11)

- [Learning Prices for Repeated Auctions with Strategic Buyers](https://mlsanity.com/paper/1311.6838/) (2013)
- [Dynamic Incentive-aware Learning: Robust Pricing in Contextual Auctions](https://mlsanity.com/paper/2002.11137/) (2020)
- [Learning in Stackelberg Games with Non-myopic Agents](https://mlsanity.com/paper/2208.09407/) (2022)
- [Auctions Between Regret-Minimizing Agents](https://mlsanity.com/paper/2110.11855/) (2021)
- [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)
- [Optimally Deceiving a Learning Leader in Stackelberg Games](https://mlsanity.com/paper/2006.06566/) (2020)
- [Learning Optimal Reserve Price against Non-myopic Bidders](https://mlsanity.com/paper/1804.11060/) (2018)
- [Imitative Follower Deception in Stackelberg Games](https://mlsanity.com/paper/1903.02917/) (2019)
- [Manipulating a Learning Defender and Ways to Counteract](https://mlsanity.com/paper/1905.11759/) (2019)
- [ABSNFT: Securitization and Repurchase Scheme for Non-Fungible Tokens Based on Game Theoretical Analysis](https://mlsanity.com/paper/2202.02199/) (2022)

## Built on by (most cited first, 3 of 3)

- [Is Knowledge Power? On the (Im)possibility of Learning from Strategic Interactions](https://mlsanity.com/paper/2408.08272/) (2024)
- [mathsfVISTA: Decentralized Machine Learning in Adversary Dominated Environments](https://mlsanity.com/paper/2605.07841/) (2026)
- [Decentralized Online Learning in General-Sum Stackelberg Games](https://mlsanity.com/paper/2405.03158/) (2024)

## Abstract (arXiv)

It is shown in recent studies that in a Stackelberg game the follower can manipulate the leader by deviating from their true best-response behavior. Such manipulations are computationally tractable and can be highly beneficial for the follower. Meanwhile, they may result in significant payoff losses for the leader, sometimes completely defeating their first-mover advantage. A warning to commitment optimizers, the risk these findings indicate appears to be alleviated to some extent by a strict information advantage the manipulations rely on. That is, the follower knows the full information about both players' payoffs whereas the leader only knows their own payoffs. In this paper, we study the manipulation problem with this information advantage relaxed. We consider the scenario where the follower is not given any information about the leader's payoffs to begin with but has to learn to manipulate by interacting with the leader. The follower can gather necessary information by querying the leader's optimal commitments against contrived best-response behaviors. Our results indicate that the information advantage is not entirely indispensable to the follower's manipulations: the follower can learn the optimal way to manipulate in polynomial time with polynomially many queries of the leader's optimal commitment.