Retention Offer Arbitration Under Capacity Constraints

Capacity should be implemented as an arbitration constraint, not as eligibility. Eligibility is for hard suitability rules, such as regulatory or product restrictions; making high-value customers eligible for the discount would remove it from everyone else and prevent trade-offs. Applicability can filter customers who should not see an offer at all. Arbitration is where offers compete, so apply a business lever that weights propensity by customer value and by remaining weekly capacity. For hard caps, use a capacity-aware arbitration or a custom constraint that decrements available volume when an offer is selected. Value prioritization should be a business lever or segment-level weight, so a high-value customer's expected retention gain can outrank a low-value customer's higher propensity. Also cap the discount's share of selections, for example 25%, to prevent early-week exhaustion. This preserves competition among offers while respecting budget.

Use a random holdout, stratified by customer value and offer eligibility, so the control group is comparable to the treated group. A 5–10% holdout is typical if retention events are frequent enough to detect the expected lift. The control group should receive no retention offer or the current standard treatment, depending on what the business is testing. The primary metric must be incremental 90-day retention, not offer acceptance, because acceptance can be high for customers who would have stayed anyway. Analyze intent-to-treat, not only customers who accepted. Check statistical power before launch and monitor for contamination. Also compare by value segment and by capacity-constrained offer. This design tells the team whether the new arbitration improves retention or merely reallocates discounts to customers who did not need them.

The propensity model learns which customers historically received or accepted offers, not the causal effect of offering them. Because discounts were over-exposed, the model may predict high discount propensity for customers who were simply targeted more often. That can amplify the same pattern and starve high-value customers. Mitigate with randomized exploration, such as a small percentage of random offer assignment, and use inverse propensity weighting when training. Consider uplift modeling to estimate incremental retention rather than acceptance. Monitor selection rates by value segment and offer type. Do not treat propensity as a causal estimate in arbitration; combine it with business rules and, where possible, validated uplift. Revalidate the model after arbitration changes, because the historical training distribution no longer matches the new decision policy.