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Over the last few years, the Shapley value, a solution concept from cooperative game theory, has found numerous applications in machine learning. In this paper, we first discuss fundamental concepts of cooperative game theory and axiomatic…

Machine Learning · Computer Science 2022-05-27 Benedek Rozemberczki , Lauren Watson , Péter Bayer , Hao-Tsung Yang , Olivér Kiss , Sebastian Nilsson , Rik Sarkar

Modern data aggregation often involves a platform collecting data from a network of users with various privacy options. Platforms must solve the problem of how to allocate incentives to users to convince them to share their data. This paper…

Machine Learning · Computer Science 2024-02-06 Justin Kang , Ramtin Pedarsani , Kannan Ramchandran

This study introduces the \emph{edge-based Shapley value}, a novel allocation rule within cooperative game theory, specifically tailored for networked systems, where value is generated through interactions represented by edges. Traditional…

Computer Science and Game Theory · Computer Science 2025-07-17 Taiki Yamada , Taisuke Matsubae , Tomoya Akamatsu

Motivated by the problem of utility allocation in a portfolio under a Markowitz mean-variance choice paradigm, we propose an allocation criterion for the variance of the sum of $n$ possibly dependent random variables. This criterion, the…

Probability · Mathematics 2017-04-04 Riccardo Colini-Baldeschi , Marco Scarsini , Stefano Vaccari

Allocating costs, benefits, and emissions fairly among power system participant entities represents a persistent challenge. The Shapley value provides an axiomatically fair solution, yet computational barriers have limited its adoption…

Systems and Control · Electrical Eng. & Systems 2025-11-04 Yuanhao Feng , Tao Sun , Yan Meng , Xuxin Yang , Donghan Feng

Data valuation -- quantifying the contribution of individual data sources to certain predictive behaviors of a model -- is of great importance to enhancing the transparency of machine learning and designing incentive systems for data…

Machine Learning · Computer Science 2023-07-28 Zhihong Liu , Hoang Anh Just , Xiangyu Chang , Xi Chen , Ruoxi Jia

We consider the design of coding schemes for the wireless two-way relaying channel when there is no channel state information at the transmitter. In the spirit of the compute and forward paradigm, we present a multilevel coding scheme that…

Information Theory · Computer Science 2016-11-17 Brett Hern , Krishna Narayanan

Suppose that $n$ computer devices are to be connected to a network via inhomogeneous Bernoulli trials. The Shapley value of a device quantifies how much the network's value increases due to the participation of that device. Characteristic…

Computer Science and Game Theory · Computer Science 2025-10-10 Jesse D Wei , Guo Wei

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

Federated learning (FL) is a popular technique to train machine learning (ML) models on decentralized data sources. In order to sustain long-term participation of data owners, it is important to fairly appraise each data source and…

Machine Learning · Computer Science 2020-09-15 Tianhao Wang , Johannes Rausch , Ce Zhang , Ruoxi Jia , Dawn Song

Shapley values have become increasingly popular in the machine learning literature thanks to their attractive axiomatisation, flexibility, and uniqueness in satisfying certain notions of `fairness'. The flexibility arises from the myriad…

Machine Learning · Statistics 2021-03-09 Daniel Vidali Fryer , Inga Strümke , Hien Nguyen

This paper addresses the benefit allocation in a mixed-energy truck platoon composed of fuel-powered and electric trucks. The interactions among trucks during platoon formation are modeled as a coalitional game with transferable utility. We…

Systems and Control · Electrical Eng. & Systems 2025-07-24 Ting Bai , Karl Henrik Johansson , Jonas Mårtensson , Andreas A. Malikopoulos

We propose the study of computing the Shapley value for a new class of cooperative games that we call budgeted games, and investigate in particular knapsack budgeted games, a version modeled after the classical knapsack problem. In these…

Computer Science and Game Theory · Computer Science 2014-09-19 Smriti Bhagat , Anthony Kim , S. Muthukrishnan , Udi Weinsberg

In cooperative games, we study how values created or costs incurred by a coalition are shared among the members within it, and the players may join the coalition in a online manner such as investors invest a startup. Recently, Ge et al.…

Computer Science and Game Theory · Computer Science 2024-10-25 Junyu Zhang , Yao Zhang , Yaoxin Ge , Dengji Zhao , Hu Fu , Zhihao Gavin Tang , Pinyan Lu

The Shapley value provides a principled framework for fairly distributing rewards among participants according to their individual contributions. While prior work has applied this concept to data valuation in machine learning, existing…

Computer Science and Game Theory · Computer Science 2026-01-22 Zhuofan Jia , Jian Pei

Originally introduced in cooperative game theory, Shapley values have become a very popular tool to explain machine learning predictions. Based on Shapley's fairness axioms, every input (feature component) gets a credit how it contributes…

Machine Learning · Statistics 2025-08-19 Michael Mayer , Mario V. Wüthrich

We investigate the distribution of the well-studied Shapley--Shubik values in weighted voting games where the agents are stochastically determined. The Shapley--Shubik value measures the voting power of an agent, in typical collective…

Computer Science and Game Theory · Computer Science 2016-01-26 Yuval Filmus , Joel Oren , Kannan Soundararajan

Shapley value is a classic notion from game theory, historically used to quantify the contributions of individuals within groups, and more recently applied to assign values to data points when training machine learning models. Despite its…

Machine Learning · Computer Science 2020-02-28 Amirata Ghorbani , Michael P. Kim , James Zou

Next generation wireless architectures are expected to enable slices of shared wireless infrastructure which are customized to specific mobile operators/services. Given infrastructure costs and the stochastic nature of mobile services'…

Networking and Internet Architecture · Computer Science 2018-05-16 Jiaxiao Zheng , Pablo Caballero , Gustavo de Veciana , Seung Jun Baek , Albert Banchs

We consider a wireless sensors network scenario where two nodes detect correlated sources and deliver them to a central collector via a wireless link. Differently from the Slepian-Wolf approach to distributed source coding, in the proposed…

Information Theory · Computer Science 2007-07-13 A. Abrardo