Fair Robust Strategic Classification under Decision-Dependent Cost Uncertainty

Humans are increasingly finding ways to strategically respond to algorithmic decision systems, raising concerns about both robustness and fairness of using AI systems in critical contexts. Existing works on fair strategic classification, which aim to address these concerns, have largely focused on static and known cost environments. We instead propose a framework for endogenously evolving and uncertain cost environments, where strategic costs evolve over time in response to past decisions. We model the firm's fair classifier design problem as a two-stage robust optimization problem with decision-dependent uncertainty and endogenously evolving costs under the demographic parity (DP)-fairness constraint. We develop an analytically supported reformulation of the fairness constraint, which enables us to solve the resulting classifier design problem. Our analysis highlights trade-offs between robustness and fairness across stages and demographic groups, notably an asymmetric robustness that preserves stronger protections from disadvantaged groups.