As multi-agent systems (MAS) become increasingly complex, identifying the contributions of individual agents is critical for system optimization. However, existing approaches lack a rigorous, unified framework for credit assignment. In this work, we formalize agent attribution as a cooperative game, parameterized by the coalition distribution, removal protocol, and target metric. Using this framework, we show that Leave-One-Out (LOO) identifies bottleneck agents as effectively as combinatorial methods, but at a fraction of the computational cost. We also demonstrate that removal protocols induce distinct games: Agent ablation isolates structural bottlenecks, whereas introspective LLM judges fail to faithfully approximate this behavior. Furthermore, to evaluate the utility of specific agent backbones, we introduce attribution via model replacement. By substituting underlying models of low-contribution agents, we improve task performance by up to 17% while reducing cost by up to 35% across three benchmarks. Finally, we apply our framework to audit a medical MAS, revealing that agent contributions to diagnostic accuracy and ethical behavior are often decoupled. By intervening on counterproductive roles, we observe an increase in ethics alignment while maintaining diagnostic accuracy. Overall, this work provides a principled approach for cost-effective MAS attribution and intervention.