Abstract

Agentic workflows solve complex tasks by orchestrating modular components (e.g., planning, reasoning, action, reflection) built on top of LLM backbones. A practical but underexplored question is model allocation: given a fixed workflow decomposition and a pool of candidate LLMs, which components should be upgraded (and with which models) to upgrade task performance, and how can we attribute gains to individual upgrades and their interactions?We present ShapleyFlow, a cooperative game theoretic framework that models component upgrades as players and evaluates component coalitions to compute Shapley values. This yields interaction-aware attribution and supports Shapley-guided configuration recommendation for model allocation under a fixed workflow structure.We further introduce CapaBench, a benchmark of 1,500+ tasks across seven domains (shopping, navigation, ticketing, mathematics, operating systems, robotic coordination, and automated theorem proving).Across 9 representative LLMs and all 2⁴ upgrade coalitions in a 4-component workflow, ShapleyFlow provides (i) principled, interaction-aware attribution for modular workflows and (ii) actionable model-allocation recommendations that improve over strong single-model baselines.