When Strategic Adaptation Improves Decisions: Causal Incentive Certificates for Decision-Focused Learning

Decision-focused learning optimizes predictions for a downstream decision but normally treats the deployment population as fixed, even when the learned rule changes which actions people take. We prove that two predictors can be identical on all historical observations and have zero historical regret while their post-response deployment losses differ by any prescribed amount. We introduce causal incentive certificates, which map downstream-aware action returns to a strongly monotone strategic equilibrium and then to a lower bound on beneficial effort. A primitive causal-decision identity derives the regret slopes from true-state effects and model-induced decision distortion and gives the smallest beneficial-effort threshold that guarantees improvement uniformly over the stated envelope. Separate smooth and hard-decision branches quantify operator misspecification, anisotropic response covariance, and normal-fan switching, while an independent selected-policy test certifies deployment without a candidate-library penalty. Across 5,000 controlled effort instances, the certificate had no violations, the primitive identity closed with maximum error below $9\times 10^{-11}$. In a UCI-based semi-synthetic study, CS-DFL achieved a worst-environment gain lower bound of $0.0496$ and a positive alignment bound under the prespecified response model.