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"How much is my data worth?" is an increasingly common question posed by organizations and individuals alike. An answer to this question could allow, for instance, fairly distributing profits among multiple data contributors and determining…

Machine Learning · Computer Science 2023-03-07 Ruoxi Jia , David Dao , Boxin Wang , Frances Ann Hubis , Nick Hynes , Nezihe Merve Gurel , Bo Li , Ce Zhang , Dawn Song , Costas Spanos

For reinforcement learning systems to be widely adopted, their users must understand and trust them. We present a theoretical analysis of explaining reinforcement learning using Shapley values, following a principled approach from game…

Machine Learning · Computer Science 2023-06-12 Daniel Beechey , Thomas M. S. Smith , Özgür Şimşek

This paper introduces the Myerson interaction index (MII), an extension of the Shapley interaction index to cooperative games with communication structures restricted by graphs. We establish a formal framework for interaction indices on…

Optimization and Control · Mathematics 2026-05-28 Jorge González-Ortega , Elisenda Molina , Juan Tejada

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

We consider a simple and altruistic multiagent system in which the agents are eager to perform a collective task but where their real engagement depends on the willingness to perform the task of other influential agents. We model this…

Computer Science and Game Theory · Computer Science 2014-03-10 Xavier Molinero , Fabián Riquelme , Maria Serna

Responsibility allocation -- determining the extent to which agents are accountable for outcomes -- is a fundamental challenge in the design and analysis of multi-agent systems. In this work, we model such systems as concurrent stochastic…

Multiagent Systems · Computer Science 2026-05-14 Chunyan Mu , Muhammad Najib

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

To reliably deploy Multi-Agent Reinforcement Learning (MARL) systems, it is crucial to understand individual agent behaviors. While prior work typically evaluates overall team performance based on explicit reward signals, it is unclear how…

Artificial Intelligence · Computer Science 2025-08-26 Ardian Selmonaj , Miroslav Strupl , Oleg Szehr , Alessandro Antonucci

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

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

Game-theoretic formulations of feature importance have become popular as a way to "explain" machine learning models. These methods define a cooperative game between the features of a model and distribute influence among these input elements…

Artificial Intelligence · Computer Science 2020-07-01 I. Elizabeth Kumar , Suresh Venkatasubramanian , Carlos Scheidegger , Sorelle Friedler

Myerson first introduced graph-restricted games in order to model the interaction of cooperative players with an underlying communication network. A dedicated solution concept -- the Myerson value -- is perhaps the most important normative…

Social and Information Networks · Computer Science 2020-01-03 Mateusz K. Tarkowski , Szymon Matejczyk , Tomasz P. Michalak , Michael Wooldridge

The burgeoning growth of the esports and multiplayer online gaming community has highlighted the critical importance of evaluating the Most Valuable Player (MVP). The establishment of an explainable and practical MVP evaluation method is…

Computer Science and Game Theory · Computer Science 2026-05-29 Haifeng Sun , Yu Xiong , Runze Wu , Kai Wang , Lan Zhang , Changjie Fan , Shaojie Tang , Xiang-Yang Li

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

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

Collaborative vehicle routing occurs when carriers collaborate through sharing their transportation requests and performing transportation requests on behalf of each other. This achieves economies of scale, thus reducing cost, greenhouse…

Machine Learning · Computer Science 2023-10-27 Stephen Mak , Liming Xu , Tim Pearce , Michael Ostroumov , Alexandra Brintrup

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

As AI usage becomes more prevalent in social contexts, understanding agent-user interaction is critical to designing systems that improve both individual and group outcomes. We present an online behavioral experiment (N = 243) in which…

Computer Science and Game Theory · Computer Science 2026-02-16 Kehang Zhu , Nithum Thain , Vivian Tsai , James Wexler , Crystal Qian

We investigate the application of the Shapley value to quantifying the contribution of a tuple to a query answer. The Shapley value is a widely known numerical measure in cooperative game theory and in many applications of game theory for…

Databases · Computer Science 2023-06-22 Ester Livshits , Leopoldo Bertossi , Benny Kimelfeld , Moshe Sebag

Most previous studies on multi-agent reinforcement learning focus on deriving decentralized and cooperative policies to maximize a common reward and rarely consider the transferability of trained policies to new tasks. This prevents such…

Machine Learning · Computer Science 2019-11-28 Heechang Ryu , Hayong Shin , Jinkyoo Park