# Learning in Repeated Multi-Objective Stackelberg Games with Payoff Manipulation

arXiv: https://arxiv.org/abs/2508.14705 · HTML: https://mlsanity.com/paper/2508.14705/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 25 references that are in the map.
- First posted on arXiv 20 Aug 2025.

## Builds on (most cited first, 14 of 14)

- [A Survey of Multi-Objective Sequential Decision-Making](https://mlsanity.com/paper/1402.0590/) (2014)
- [Multi-Objective Multi-Agent Decision Making: A Utility-based Analysis and Survey](https://mlsanity.com/paper/1909.02964/) (2019)
- [Adaptive Contract Design for Crowdsourcing Markets: Bandit Algorithms for Repeated Principal-Agent Problems](https://mlsanity.com/paper/1405.2875/) (2014)
- [A Unifying Perspective on Multi-Calibration: Game Dynamics for Multi-Objective Learning](https://mlsanity.com/paper/2302.10863/) (2023)
- [Learning in Stackelberg Games with Non-myopic Agents](https://mlsanity.com/paper/2208.09407/) (2022)
- [Learning to Play Sequential Games versus Unknown Opponents](https://mlsanity.com/paper/2007.05271/) (2020)
- [Online Learning in Stackelberg Games with an Omniscient Follower](https://mlsanity.com/paper/2301.11518/) (2023)
- [Incentivized Learning in Principal-Agent Bandit Games](https://mlsanity.com/paper/2403.03811/) (2024)
- [A utility-based analysis of equilibria in multi-objective normal form games](https://mlsanity.com/paper/2001.08177/) (2020)
- [Maximizing utility in multi-agent environments by anticipating the behavior of other learners](https://mlsanity.com/paper/2407.04889/) (2024)
- [Repeated Principal-Agent Games with Unobserved Agent Rewards and Perfect-Knowledge Agents](https://mlsanity.com/paper/2304.07407/) (2023)
- [Preference Communication in Multi-Objective Normal-Form Games](https://mlsanity.com/paper/2111.09191/) (2021)
- [Learning to Incentivize in Repeated Principal-Agent Problems with Adversarial Agent Arrivals](https://mlsanity.com/paper/2505.23124/) (2025)
- [No-Regret Learning in Stackelberg Games with an Application to Electric Ride-Hailing](https://mlsanity.com/paper/2504.03745/) (2025)

## Abstract (arXiv)

We study payoff manipulation in repeated multi-objective Stackelberg games, where a leader may strategically influence a follower's deterministic best response, e.g., by offering a share of their own payoff. We assume that the follower's utility function, representing preferences over multiple objectives, is unknown but linear, and its weight parameter must be inferred through interaction. This introduces a sequential decision-making challenge for the leader, who must balance preference elicitation with immediate utility maximisation. We formalise this problem and propose manipulation policies based on expected utility (EU) and long-term expected utility (longEU), which guide the leader in selecting actions and offering incentives that trade off short-term gains with long-term impact. We prove that under infinite repeated interactions, longEU converges to the optimal manipulation. Empirical results across benchmark environments demonstrate that our approach improves cumulative leader utility while promoting mutually beneficial outcomes, all without requiring explicit negotiation or prior knowledge of the follower's utility function.