# Understanding and Optimizing Agentic Workflows via Shapley value

arXiv: https://arxiv.org/abs/2502.00510 · HTML: https://mlsanity.com/paper/2502.00510/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Software engineering coding agents, one of 16 directions in LLM agents and tool use.
- Builds on 8 of its 30 references that are in the map.
- First posted on arXiv 1 Feb 2025.

## Placed in

- LLM agents and tool use / [Software engineering coding agents](https://mlsanity.com/agents/software-engineering-coding-agents/)

## Builds on (most cited first, 8 of 8)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Chatbot Arena: An Open Platform for Evaluating LLMs by Human Preference](https://mlsanity.com/paper/2403.04132/) (2024)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [shapiq: Shapley Interactions for Machine Learning](https://mlsanity.com/paper/2410.01649/) (2024)
- [MMAU: A Holistic Benchmark of Agent Capabilities Across Diverse Domains](https://mlsanity.com/paper/2407.18961/) (2024)

## Built on by (most cited first, 10 of 10)

- [AgentNet: Decentralized Evolutionary Coordination for LLM-based Multi-Agent Systems](https://mlsanity.com/paper/2504.00587/) (2025)
- [A Survey of AI Agent Protocols](https://mlsanity.com/paper/2504.16736/) (2025)
- [Game Theory Meets Large Language Models: A Systematic Survey with Taxonomy and New Frontiers](https://mlsanity.com/paper/2502.09053/) (2025)
- [Agent Exchange: Shaping the Future of AI Agent Economics](https://mlsanity.com/paper/2507.03904/) (2025)
- [Evolutionary Perspectives on the Evaluation of LLM-Based AI Agents: A Comprehensive Survey](https://mlsanity.com/paper/2506.11102/) (2025)
- [Who Gets the Reward & Who Gets the Blame? Evaluation-Aligned Training Signals for Multi-LLM Agents](https://mlsanity.com/paper/2511.10687/) (2025)
- [Towards Feedback-to-Plan Decisions for Self-Evolving LLM Agents in CUDA Kernel Generation](https://mlsanity.com/paper/2605.26720/) (2026)
- [DynaTree: Dynamic Agentic Retrieval Tree for Time-Sensitive News Retrieval](https://mlsanity.com/paper/2605.31377/) (2026)
- [Semantic Cooperative Games for Contribution Attribution in LLM-Based Multi-Agent Systems](https://mlsanity.com/paper/2607.18255/) (2026)
- [Compositional RL: Evaluating and Training LLMs for Collaborative Reasoning](https://mlsanity.com/paper/2610.17456/) (2026)

## Abstract (arXiv)

Agentic workflows have become the dominant paradigm for building complex AI systems, orchestrating specialized components, such as planning, reasoning, action execution, and reflection, to tackle sophisticated real-world tasks. However, systematically analyzing and optimizing these workflows remains challenging due to intricate component interdependencies and the lack of principled attribution methods. In this work, we introduce ShapleyFlow, the first framework that employs cooperative game theory to analyze and optimize agentic workflows. By applying the Shapley value to evaluate all possible component configurations, ShapleyFlow enables fine-grained attribution of each component's contribution and facilitates the identification of task-specific optimal configurations. Through a constructed dataset evaluated across 7 scenarios, such as navigation, math and OS, we demonstrate 3 key contributions: (1) Theoretical Framework: a principled game-theoretic approach for the attribution of contributions in agentic workflows. (2) Optimal Workflow Discovery: ShapleyFlow identifies task-specific component configurations that consistently outperform workflows relying on a single LLM across all tested tasks. (3) Comprehensive Analysis: we construct and analyze over 1,500 tasks, providing actionable insights and design guidelines for optimizing workflows across multiple domains.