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Related papers: The Shapley Value in Knapsack Budgeted Games

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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

Agentic workflows have become the dominant paradigm for building complex AI systems, orchestrating specialized components, such as planning, reasoning, action execution, and reflection, to tackle sophisticated real-world tasks. However,…

Multi-agent reinforcement learning is an area of rapid advancement in artificial intelligence and machine learning. One of the important questions to be answered is how to conduct credit assignment in a multi-agent system. There have been…

Multiagent Systems · Computer Science 2024-02-26 Jianhong Wang

A number of techniques have been proposed to explain a machine learning model's prediction by attributing it to the corresponding input features. Popular among these are techniques that apply the Shapley value method from cooperative game…

Machine Learning · Computer Science 2020-06-29 Luke Merrick , Ankur Taly

We introduce a class of cooperative games induced by weighted directed graphs. Specifically, the coalitional value combines an internal interaction term given by the induced subgraph game with an external component based on minimal incoming…

Computer Science and Game Theory · Computer Science 2026-05-19 David Ryzák , Tomáš Kroupa

Designing fair compensation mechanisms for demand response (DR) is challenging. This paper models the problem in a game theoretic setting and designs a payment distribution mechanism based on the Shapley Value. As exact computation of the…

Computer Science and Game Theory · Computer Science 2014-03-27 Gearóid O'Brien , Abbas El Gamal , Ram Rajagopal

In many multi-agent settings, participants can form teams to achieve collective outcomes that may far surpass their individual capabilities. Measuring the relative contributions of agents and allocating them shares of the reward that…

Machine Learning · Computer Science 2022-08-19 Daphne Cornelisse , Thomas Rood , Mateusz Malinowski , Yoram Bachrach , Tal Kachman

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 a game-theoretic notion for wealth distribution that is nowadays extensively used to explain complex data-intensive computation, for instance, in network analysis or machine learning. Recent theoretical works show that…

Databases · Computer Science 2022-01-04 Daniel Deutch , Nave Frost , Benny Kimelfeld , Mikaël Monet

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 study the Shapley value in weighted voting games. The Shapley value has been used as an index for measuring the power of individual agents in decision-making bodies and political organizations, where decisions are made by a majority vote…

Computer Science and Game Theory · Computer Science 2014-08-05 Joel Oren , Yuval Filmus , Yair Zick , Yoram Bachrach

One of the long-debated issues in coalitional game theory is how to extend the Shapley value to games with externalities (partition-function games). When externalities are present, not only can a player's marginal contribution - a central…

Computer Science and Game Theory · Computer Science 2013-08-29 Oskar Skibski , Tomasz P. Michalak , Michael Wooldridge

The Reward-Penalty-Selection Problem (RPSP) can be seen as a combination of the Set Cover Problem (SCP) and the Hitting Set Problem (HSP). Given a set of elements, a set of reward sets, and a set of penalty sets, one tries to find a subset…

Computer Science and Game Theory · Computer Science 2022-01-17 Niklas Gräf , Till Heller , Sven O. Krumke

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

Budget aggregation deals with the social choice problem of distributing an exogenously given budget among a set of public projects, given agents' preferences. Taking a game-theoretic perspective, we study budget-aggregation games where each…

Computer Science and Game Theory · Computer Science 2026-02-25 Patrick Becker , Alexander Fries , Matthias Greger , Erel Segal-Halevi

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

Big Boss Games represent a specific class of cooperative games where a single veto player, known as the Big Boss, plays a central role in determining resource allocation and maintaining coalition stability. In this paper, we introduce a…

Computer Science and Game Theory · Computer Science 2025-03-26 Luis A. Guardiola , Ana Meca

A quantitative assessment of the global importance of an agent in a team is as valuable as gold for strategists, decision-makers, and sports coaches. Yet, retrieving this information is not trivial since in a cooperative task it is hard to…

Artificial Intelligence · Computer Science 2022-12-21 Giorgio Angelotti , Natalia Díaz-Rodríguez

Electing a committee of size k from m alternatives (k < m) is an interesting problem under the multi-winner voting rules. However, very few committee selection rules found in the literature consider the coalitional possibilities among the…

Theoretical Economics · Economics 2023-08-08 Ritu Dutta , Rajnish Kumnar , Surajit Borkotokey

According to Shapley's game-theoretical result, there exists a unique game value of finite cooperative games that satisfies axioms on additivity, efficiency, null-player property and symmetry. The original setting requires symmetry with…

Computer Science and Game Theory · Computer Science 2013-08-29 Ales Antonin Kubena , Peter Franek