Large language models increasingly generate multiple retrieval actions jointly, while downstream systems often provide only one reward for the resulting set. Broadcasting this reward provides a valid score-function gradient estimator for the expected set-level objective, but does not determine a coalition-dependent within-set attribution. We introduce CASI (Credit Assignment via Set Intervention for Agentic Retrieval), which constructs the missing counterfactual information through snapshot-grounded set intervention: generate and retrieve once, hold replayable snapshot components fixed, and evaluate alternative subsets under common conditions. Shapley aggregation converts these marginals into within-set credit, which bounded zero-sum advantage shaping incorporates into policy optimization. For m >= 4, singleton, leave-one-out, and full-set endpoints do not generally determine the Shapley allocation; under additive set values, extra coalition evaluations are redundant. In a five-action sponsored-search setting, exhaustive auction replay over 1,200 requests reveals substantial coalition dependence. Under the training-time evaluator, CASI achieves the highest median cosine similarity to a replay-defined Shapley reference among evaluated credit rules; under a sensitivity backend, CASI does not outperform Singleton. Across five independent training runs, CASI-trained policies achieve higher held-out auction-replay set value than Singleton- or Broadcast-trained policies. In a randomized seven-day production A/B test on 10% of traffic, the CASI-trained policy yields an observed 3.51% lift in the primary advertiser-value metric over production control.

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