This paper studies reward manipulation, a strategy by which a leader can strategically influence a follower's optimal deterministic response, for example, by sharing their own rewards, in an iterated multi-objective Stackelberg game. The follower's utility function (representing their preferences for multiple objectives) is assumed to be linear, though unknown, and its weighting parameters must be inferred through interactions. This presents the leader with a sequential decision-making task: balancing immediate utility maximization with preference induction. This paper formalizes this problem and proposes a manipulation policy based on expected utility (EU) and long-term expected utility (longEU). This strategy guides the leader in selecting actions and providing incentives by balancing short-term gains with long-term impact. We demonstrate that longEU converges to optimal manipulation under infinitely repeated interactions. Empirical results in a baseline environment demonstrate that our approach enhances cumulative leader utility while promoting mutually beneficial outcomes, even without explicit negotiation or prior knowledge of the follower's utility function.
