As predictive models are deployed into the real world, they must increasingly contend with strategic behavior. A growing body of work on strategic classification treats this problem as a Stackelberg game: the decision-maker "leads" in the game by deploying a model, and the strategic agents "follow" by playing their best response to the deployed model. Importantly, in this framing, the burden of learning is placed solely on the decision-maker, while the agents' best responses are implicitly treated as instantaneous. In this work, we argue that the order of play in strategic classification is fundamentally determined by the relative frequencies at which the decision-maker and the agents adapt to each other's actions. In particular, by generalizing the standard model to allow both players to learn over time, we show that a decision-maker that makes updates faster than the agents can reverse the order of play, meaning that the agents lead and the decision-maker follows. We observe in standard learning settings that such a role reversal can be desirable for both the decision-maker and the strategic agents. Finally, we show that a decision-maker with the freedom to choose their update frequency can induce learning dynamics that converge to Stackelberg equilibria with either order of play.

本文针对战略分类中的决策者和策略代理人的适应行为，通过引入双方适应行为的相对频率，证明了决策者较快地更新可以改变角色顺序，从而导致代理人领导，决策者跟随，并进一步展示了决策者在某些更新频率下可诱导收敛于任何角色顺序下的 Stackelberg 平衡。

战略分类中谁主导谁跟随？