However, in open-ended environments lacking coordination rules, agents tend to act in self-interested ways. The central challenge in achieving coordination lies in credit assignment--fairly evaluating each agent's contribution and designing pricing mechanisms that align their heterogeneous goals. This problem is critical as LLMs increasingly participate in complex human-AI collaborations, where fair compensation and accountability rely on effective pricing mechanisms. Inspired by how human societies address similar coordination challenges (e.g., via temporary collaborations like employment or subcontracting), a cooperative workflow Shapley-Coop is proposed. ShapleyCoop integrates Shapley Chain-of-Thought--leveraging marginal contributions as a principled basis for pricing--with structured negotiation protocols for effective price matching, enabling LLM agents to coordinate through rational task-time pricing and post-task reward redistribution. This approach aligns agent incentives, fosters cooperation, and maintains autonomy. We evaluate Shapley-Coop across two multi-agent games and a software engineering simulation, demonstrating that it consistently enhances LLM agent collaboration and facilitates equitable credit assignment.

Data valuation quantifies the impact of individual data points on model performance, and Shapley values provide a principled approach to this important task due to their desirable axiomatic properties, albeit with high computational complexity. Recent breakthroughs have enabled fast computation of exact Shapley values for unweighted k-nearest neighbor (kNN) classifiers. However, extending this to weighted kNN models has remained a significant open challenge. The state-of-theart methods either require quadratic time complexity or resort to approximation via sampling. In this paper, we show that a conceptually simple but overlooked approach -- data duplication -- can be applied to this problem, yielding a natural variant of weighted kNN-Shapley. However, a straightforward application of the data-duplication idea leads to increased data size and prohibitive computational and memory costs. We develop an efficient algorithm that avoids materializing the duplicated dataset by exploiting the structural properties of weighted kNN models, reducing the complexity to near-linear time in the original data size. Besides, we establish theoretical foundations for this approach through axiomatic characterization of the resulting values, and empirically validate the effectiveness and efficiency of our method.

Then we give more experimental results on CIFAR-100 and stability analysis of Shapley value (Appendix B). Finally, we add properties of the Shapley value and proof of decomposition of CNNs in frequency domain (Appendix D). In this section, we introduce the details of the Shapley value sampling. A.1 Details of the Model for the Shapley Value Sampling We sample the Shapley value for models trained on CIFAR10, CIFAR100 and ImageNet. For CIFAR10 and CIFAR100, we employ ResNet-18 and train them ourselves.

We consider the problem of optimization from samples of monotone submodular functions with bounded curvature. In numerous applications, the function optimized is not known a priori, but instead learned from data. What are the guarantees we have when optimizing functions from sampled data? In this paper we show that for any monotone submodular function with curvature c there is a (1 c)/(1 + c c2) approximation algorithm for maximization under cardinality constraints when polynomially-many samples are drawn from the uniform distribution over feasible sets. Moreover, we show that this algorithm is optimal. That is, for any c< 1, there exists a submodular function with curvature c for which no algorithm can achieve a better approximation. The curvature assumption is crucial as for general monotone submodular functions no algorithm can obtain a constant-factor approximation for maximization under a cardinality constraint when observing polynomially-many samples drawn from any distribution over feasible sets, even when the function is statistically learnable.

Several data valuation algorithms have been proposed to quantify data quality, however, there lacks a systemic and standardized benchmarking system for data valuation.

Maximum target coverage by adjusting the orientation of distributed sensors is an important problem in directional sensor networks (DSNs).