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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

The Shapley value---probably the most important normative payoff division scheme in coalitional games---has recently been advocated as a useful measure of centrality in networks. However, although this approach has a variety of real-world…

Computer Science and Game Theory · Computer Science 2014-02-05 Tomasz Pawel Michalak , Karthik V Aadithya , Piotr L. Szczepanski , Balaraman Ravindran , Nicholas R. Jennings

The Shapley value (SV) and Least core (LC) are classic methods in cooperative game theory for cost/profit sharing problems. Both methods have recently been proposed as a principled solution for data valuation tasks, i.e., quantifying the…

Machine Learning · Computer Science 2022-04-08 Tianhao Wang , Yu Yang , Ruoxi Jia

As data becomes the fuel driving technological and economic growth, a fundamental challenge is how to quantify the value of data in algorithmic predictions and decisions. For example, in healthcare and consumer markets, it has been…

Machine Learning · Statistics 2019-06-11 Amirata Ghorbani , James Zou

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

Shapley value is a popular approach for measuring the influence of individual features. While Shapley feature attribution is built upon desiderata from game theory, some of its constraints may be less natural in certain machine learning…

Machine Learning · Computer Science 2022-09-28 Yongchan Kwon , James Zou

Shapley value is originally a concept in econometrics to fairly distribute both gains and costs to players in a coalition game. In the recent decades, its application has been extended to other areas such as marketing, engineering and…

Machine Learning · Statistics 2023-09-19 Liuqing Yang , Yongdao Zhou , Haoda Fu , Min-Qian Liu , Wei Zheng

The Shapley value is arguably the most central normative solution concept in cooperative game theory. It specifies a unique way in which the reward from cooperation can be "fairly" divided among players. While it has a wide range of real…

Computer Science and Game Theory · Computer Science 2014-02-14 Sasan Maleki , Long Tran-Thanh , Greg Hines , Talal Rahwan , Alex Rogers

This paper re-examines the Shapley value methods for attribution analysis in the area of online advertising. As a credit allocation solution in cooperative game theory, Shapley value method directly quantifies the contribution of online…

Econometrics · Economics 2018-04-17 Kaifeng Zhao , Seyed Hanif Mahboobi , Saeed R. Bagheri

In this paper, we address the problem of fair sharing of the total value of a crowd-sourced network system between major participants (founders) and minor participants (crowd) using cooperative game theory. Shapley allocation is regarded as…

Computer Science and Game Theory · Computer Science 2023-05-23 Mishal Assif P K , William Kennedy , Iraj Saniee

Distributional data Shapley value (DShapley) has recently been proposed as a principled framework to quantify the contribution of individual datum in machine learning. DShapley develops the foundational game theory concept of Shapley values…

Machine Learning · Statistics 2021-02-19 Yongchan Kwon , Manuel A. Rivas , James Zou

The Shapley value is the prevalent solution for fair division problems in which a payout is to be divided among multiple agents. By adopting a game-theoretic view, the idea of fair division and the Shapley value can also be used in machine…

Computer Science and Game Theory · Computer Science 2026-05-13 Guilherme Dean Pelegrina , Patrick Kolpaczki , Eyke Hüllermeier

Following the original interpretation of the Shapley value (Shapley, 1953a) as a priori evaluation of the prospects of a player in a multi-person interaction situation, we propose a group value, which we call the Shapley group value, as a…

Optimization and Control · Mathematics 2014-12-18 Ramón Flores , Elisenda Molina , Juan Tejada

The latest developments in AI focus on agentic systems where artificial and human agents cooperate to realize global goals. An example is collaborative learning, which aims to train a global model based on data from individual agents. A…

Computer Science and Game Theory · Computer Science 2025-08-20 Björn Filter , Ralf Möller , Özgür Lütfü Özçep

We introduce a variable importance measure to quantify the impact of individual input variables to a black box function. Our measure is based on the Shapley value from cooperative game theory. Many measures of variable importance operate by…

Machine Learning · Computer Science 2020-10-05 Masayoshi Mase , Art B. Owen , Benjamin Seiler

In this dissertation, we analyze the computational properties of game-theoretic centrality measures. The key idea behind game-theoretic approach to network analysis is to treat nodes as players in a cooperative game, where the value of each…

Computer Science and Game Theory · Computer Science 2015-12-08 Piotr Lech Szczepański

The Shapley value has become popular in the Explainable AI (XAI) literature, thanks, to a large extent, to a solid theoretical foundation, including four "favourable and fair" axioms for attribution in transferable utility games. The…

Machine Learning · Computer Science 2021-02-23 Daniel Fryer , Inga Strümke , Hien Nguyen

We show that any cooperative game can be represented by an assignment of costly facilities to players, in which it is intuitively obvious how to allocate the total cost in an equitable manner. This equitable solution turns out to be the…

Theoretical Economics · Economics 2024-01-19 Pradeep Dubey

The Shapley value is a common tool in game theory to evaluate the importance of a player in a cooperative setting. In a geometric context, it provides a way to measure the contribution of a geometric object in a set towards some function on…

Computational Geometry · Computer Science 2020-02-14 Shuhao Tan

In the classical context, the cooperative game theory concept of the Shapley value has been adapted for post hoc explanations of machine learning models. However, this approach does not easily translate to eXplainable Quantum ML (XQML).…

Emerging Technologies · Computer Science 2024-11-05 Iain Burge , Michel Barbeau , Joaquin Garcia-Alfaro