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Explainability and fairness have mainly been considered separately, with recent exceptions trying the explain the sources of unfairness. This paper shows that the Shapley value can be used to both define and explain unfairness, under…

Machine Learning · Computer Science 2026-03-31 Fadoua Amri-Jouidel , Emmanuel Kemel , Stéphane Mussard

An important problem in project management is determining ways to distribute amongst activities the costs that are incurred when a project is delayed because some activities end later than expected. In this study, we address this problem in…

Computer Science and Game Theory · Computer Science 2024-02-01 J. C. Gonçalves-Dosantos , I. García-Jurado , J. Costa

This paper studies an energy storage (ES) sharing model which is cooperatively invested by multiple buildings for harnessing on-site renewable utilization and grid price arbitrage. To maximize the economic benefits, we jointly consider the…

Computer Science and Game Theory · Computer Science 2021-04-06 Yu Yang , Guoqiang Hu , Costas J. Spanos

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

From social contracts to climate agreements, individuals engage in groups that must collectively reach decisions with varying levels of equality and fairness. These dilemmas also pervade Distributed Artificial Intelligence, in domains such…

This paper generalizes L.S. Shapley's celebrated value allocation theory on coalition games by discovering and applying a fundamental connection between stochastic path integration driven by canonical time-reversible Markov chains and…

Probability · Mathematics 2022-01-04 Tongseok Lim

In this paper, we propose and analyse two game theoretical models useful to design marketing channels attribution mechanisms based on cooperative TU games and bankruptcy problems, respectively. First, we analyse the Sum Game, a coalitional…

Theoretical Economics · Economics 2020-12-03 Elisenda Molina , Juan Tejada , Tom Weiss

As the decisions made or influenced by machine learning models increasingly impact our lives, it is crucial to detect, understand, and mitigate unfairness. But even simply determining what "unfairness" should mean in a given context is…

Machine Learning · Computer Science 2020-10-16 Tom Begley , Tobias Schwedes , Christopher Frye , Ilya Feige

The Shapley value, which is arguably the most popular approach for assigning a meaningful contribution value to players in a cooperative game, has recently been used intensively in explainable artificial intelligence. Its meaningfulness is…

Machine Learning · Computer Science 2024-01-31 Patrick Kolpaczki , Viktor Bengs , Maximilian Muschalik , Eyke Hüllermeier

We study the design and approximation of optimal crowdsourcing contests. Crowdsourcing contests can be modeled as all-pay auctions because entrants must exert effort up-front to enter. Unlike all-pay auctions where a usual design objective…

Computer Science and Game Theory · Computer Science 2011-11-15 Shuchi Chawla , Jason D. Hartline , Balasubramanian Sivan

We argue that using the Shapley value of cooperative game theory as the scheme for risk allocation among non-orthogonal risk factors is a natural way of interpreting the contribution made by each of such factors to overall portfolio risk.…

Computational Finance · Quantitative Finance 2021-03-10 Patrick S. Hagan , Andrew Lesniewski , Georgios E. Skoufis , Diana E. Woodward

We take an axiomatic approach to the allocation of riparian water rights. We formalize ethical or structural properties as axioms of allocation rules. We show that several combinations of these axioms characterize focal rules implementing…

Theoretical Economics · Economics 2025-12-01 Ricardo Martinez , Juan D. Moreno-Ternero

What is the value of an individual model in an ensemble of binary classifiers? We answer this question by introducing a class of transferable utility cooperative games called \textit{ensemble games}. In machine learning ensembles,…

Machine Learning · Computer Science 2021-06-14 Benedek Rozemberczki , Rik Sarkar

In this paper the Shapley value of digraph (directed graph) games are considered. Digraph games are transferable utility (TU) games with limited cooperation among players, where players are represented by nodes. A restrictive relation…

Computer Science and Game Theory · Computer Science 2017-06-09 Krishna Khatri

Public Goods Games represent one of the most useful tools to study group interactions between individuals. However, even if they could provide an explanation for the emergence and stability of cooperation in modern societies, they are not…

Physics and Society · Physics 2016-05-05 Sandro Meloni , Cheng-Yi Xia , Yamir Moreno

Cooperative game is a critical research area in the multi-agent reinforcement learning (MARL). Global reward game is a subclass of cooperative games, where all agents aim to maximize the global reward. Credit assignment is an important…

Machine Learning · Computer Science 2022-10-14 Jianhong Wang , Yuan Zhang , Tae-Kyun Kim , Yunjie Gu

Additive feature explanations using Shapley values have become popular for providing transparency into the relative importance of each feature to an individual prediction of a machine learning model. While Shapley values provide a unique…

Machine Learning · Computer Science 2021-12-21 Thomas W. Campbell , Heinrich Roder , Robert W. Georgantas , Joanna Roder

The purpose of this study is to propose a model that predicts the social and psychological factors that affect the individuals collaborative learning outcome in group projects. The model is established on the basis of two theories, namely,…

Computers and Society · Computer Science 2016-10-18 Sara Taraman , Yasmin Hassan , Doaa Shawky , Ashraf H. Badawi

A set of divisible resources becomes available over a sequence of rounds and needs to be allocated immediately and irrevocably. Our goal is to distribute these resources to maximize fairness and efficiency. Achieving any non-trivial…

Computer Science and Game Theory · Computer Science 2020-09-29 Vasilis Gkatzelis , Alexandros Psomas , Xizhi Tan

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