Learning in Repeated Multi-Objective Stackelberg Games with Payoff Manipulation
This addresses sequential decision-making in strategic interactions for applications like economics or AI systems, but it is incremental as it builds on existing Stackelberg game frameworks with payoff manipulation.
The paper tackles the problem of a leader strategically manipulating payoffs in repeated multi-objective Stackelberg games to influence a follower's best response, without prior knowledge of the follower's utility function, and shows that their proposed long-term expected utility policy converges to optimal manipulation and improves cumulative leader utility in benchmark environments.
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.