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Incentives for early arrival (I4EA) was recently proposed for studying online cooperative games. In an online cooperative game, players arrive in an unknown order, and the value increase after each player arrived should be distributed…

Computer Science and Game Theory · Computer Science 2025-11-17 Yaoxin Ge , Yao Zhang , Dengji Zhao

Collaborative machine learning (ML) is an appealing paradigm to build high-quality ML models by training on the aggregated data from many parties. However, these parties are only willing to share their data when given enough incentives,…

Machine Learning · Computer Science 2020-10-27 Rachael Hwee Ling Sim , Yehong Zhang , Mun Choon Chan , Bryan Kian Hsiang Low

This paper proposes a novel approach to explain the predictions made by data-driven methods. Since such predictions rely heavily on the data used for training, explanations that convey information about how the training data affects the…

Machine Learning · Statistics 2022-12-09 Andreas Brandsæter , Ingrid K. Glad

Data valuation using Shapley value has emerged as a prevalent research domain in machine learning applications. However, it is a challenge to address the role of order in data cooperation as most research lacks such discussion. To tackle…

Machine Learning · Computer Science 2023-05-04 Jie Liu , Peizheng Wang , Chao Wu

Centralized Training with Decentralized Execution (CTDE) has been a popular paradigm in cooperative Multi-Agent Reinforcement Learning (MARL) settings and is widely used in many real applications. One of the major challenges in the training…

Artificial Intelligence · Computer Science 2022-01-25 Jiahui Li , Kun Kuang , Baoxiang Wang , Furui Liu , Long Chen , Fei Wu , Jun Xiao

Shapley values have become one of the go-to methods to explain complex models to end-users. They provide a model agnostic post-hoc explanation with foundations in game theory: what is the worth of a player (in machine learning, a feature…

Machine Learning · Computer Science 2023-06-21 Joran Michiels , Maarten De Vos , Johan Suykens

The assignment game, introduced by Shapley and Shubik (1971), is a classic model for two-sided matching markets between buyers and sellers. In the original assignment game, it is assumed that payments lead to transferable utility and that…

Discrete Mathematics · Computer Science 2025-04-01 Eric Balkanski , Christopher En , Yuri Faenza

We propose a variant of the Shapley value, the group Shapley value, to interpret counterfactual simulations in structural economic models by quantifying the importance of different components. Our framework compares two sets of parameters,…

Econometrics · Economics 2024-10-10 Yongchan Kwon , Sokbae Lee , Guillaume A. Pouliot

Following the work of Lloyd Shapley on the Shapley value, and tangentially the work of Guillermo Owen, we offer an alternative non-probabilistic formulation of part of the work of Robert J. Weber in his 1978 paper "Probabilistic values for…

Theoretical Economics · Economics 2019-05-13 Jacob North Clark , Stephen Montgomery-Smith

Shapley-based data valuation provides a principled way to quantify the contribution of training data, but its high computational cost makes it impractical in dynamic settings where tasks and training players evolve. Existing methods treat…

Machine Learning · Computer Science 2026-05-21 Xuan Yang , Hsi-Wen Chen , Ming-Syan Chen , Jian Pei

Explaining AI systems is fundamental both to the development of high performing models and to the trust placed in them by their users. The Shapley framework for explainability has strength in its general applicability combined with its…

Machine Learning · Statistics 2021-12-21 Christopher Frye , Colin Rowat , Ilya Feige

Motivated by the markets operating on fast time scales, we present a framework for online coalitional games with time-varying coalitional values and propose real-time payoff distribution mechanisms. Specifically, we design two online…

Systems and Control · Electrical Eng. & Systems 2023-01-31 Aitazaz Ali Raja , Sergio Grammatico

Current practice in interpretable machine learning often focuses on explaining the final model trained from data, e.g., by using the Shapley additive explanations (SHAP) method. The recently developed Shapley variable importance cloud…

Machine Learning · Computer Science 2022-12-19 Yilin Ning , Mingxuan Liu , Nan Liu

With the development of sensing and communication technologies in networked cyber-physical systems (CPSs), multi-agent reinforcement learning (MARL)-based methodologies are integrated into the control process of physical systems and…

Computer Science and Game Theory · Computer Science 2022-06-16 Songyang Han , He Wang , Sanbao Su , Yuanyuan Shi , Fei Miao

Model interpretability is one of the most intriguing problems in most of the Machine Learning models, particularly for those that are mathematically sophisticated. Computing Shapley Values are arguably the best approach so far to find the…

Machine Learning · Statistics 2022-04-15 Indranil Basu , Subhadip Maji

With the adoption of machine learning-based solutions in routine clinical practice, the need for reliable interpretability tools has become pressing. Shapley values provide local explanations. The method gained popularity in recent years.…

Methodology · Statistics 2023-06-27 Lucile Ter-Minassian , Sahra Ghalebikesabi , Karla Diaz-Ordaz , Chris Holmes

The Shapley value equals a player's contribution to the potential of a game. The potential is a most natural one-number summary of a game, which can be computed as the expected accumulated worth of a random partition of the players. This…

Theoretical Economics · Economics 2024-07-23 André Casajus , Yukihiko Funaki , Frank Huettner

The idea of approximating the Shapley value of an n-person game by Monte Carlo simulation was first suggested by Mann and Shapley (1960) and they also introduced four different heuristical methods to reduce the estimation error. Since 1960,…

Computer Science and Game Theory · Computer Science 2022-04-20 Ferenc Illés , Péter Kerényi

Motivated by the fact that the worth of a coalition may depend on the order in which agents arrive, Nowak and Radzik (1994) (NR) introduced cooperative games with generalized characteristic functions. We study such temporal cooperative…

Computer Science and Game Theory · Computer Science 2026-03-17 Ashwin Goyal , Drashthi Doshi , Swaprava Nath

Feature attribution for kernel methods is often heuristic and not individualised for each prediction. To address this, we turn to the concept of Shapley values~(SV), a coalition game theoretical framework that has previously been applied to…

Machine Learning · Statistics 2022-05-27 Siu Lun Chau , Robert Hu , Javier Gonzalez , Dino Sejdinovic