Large Language Models (LLMs) excel at multi-step reasoning, yet current parallel reasoning approaches often fail to distinguish the contributions of individual reasoning paths. Many paths may be redundant, misleading, or even detrimental, but outcome-level rewards assign uniform reward, leading to ambiguous learning signals and unstable training. We propose Parallel Shapley, a reinforcement learning framework that attributes fine-grained, path-level contributions in multi-path reasoning. Treating each path as a player in a cooperative game, we leverage Shapley values to quantify marginal contributions, using a generative reward model to evaluate path utilities and Monte Carlo sampling for efficient approximation. Experiments on mathematical reasoning benchmarks show that Parallel Shapley outperforms existing baselines while providing more stable and interpretable training. Our framework effectively "fishes out the free riders," assigning reward proportionally and improving multi-path reasoning in LLMs.
Cooperative multi-agent RL systems routinely use team-averaged rewards, a feedback-attribution choice that gives each agent the team outcome regardless of its individual contribution. We ask whether this leaves a measurable signature, geometric or behavioral, on learned representations. We propose EffRank/$n$ (effective rank normalized by agent count) and $D_\text{act}$ (mean pairwise KL divergence between agents' action distributions) as low-overhead diagnostics for reward-attribution effects, then test them on competent MAPPO agents in SMACv2 \texttt{protoss\_5\_vs\_5}, where unit type is encoded in the observation. In an observation $\times$ reward-attribution comparison (unit type observed vs.\ masked; individual damage-contribution reward vs.\ shared team reward), geometry follows observation rather than reward. With unit type observed, shared and individual rewards have similar EffRank/$n$ ($0.31{\pm}0.03$ vs.\ $0.29{\pm}0.02$) and probe accuracy ($0.75{\pm}0.05$ vs.\ $0.73{\pm}0.05$, both $\gg 1/3$ chance), while $D_\text{act}$ leans higher under individual rewards ($1.23{\pm}0.06$ vs.\ $1.07{\pm}0.20$). Masking unit type cuts the above-chance probe signal by more than half, to $0.49$ in both reward arms. In short: individually rewarded agents are competent and separable by role, but on SMACv2 the observation explains the geometry and reward attribution shows up mainly in behavior. Thus geometric diagnostics must control for observed role information and test persistent roles that are not directly observed. EffRank/$n$ and $D_\text{act}$ add $<$5\% overhead.