Related papers: The Shapley group value
Can we predict how well a team of individuals will perform together? How should individuals be rewarded for their contributions to the team performance? Cooperative game theory gives us a powerful set of tools for answering these questions:…
We show that a cooperative game may be decomposed into a sum of component games, one for each player, using the combinatorial Hodge decomposition on a graph. This decomposition is shown to satisfy certain efficiency, null-player, symmetry,…
Facility location games have been a topic of major interest in economics, operations research and computer science, starting from the seminal work by Hotelling. Spatial facility location models have successfully predicted the outcome of…
This paper introduces a measure of uncertainty in the determination of the Shapley value, illustrates it with examples, and studies some of its properties. The introduced measure of uncertainty quantifies random variations in a player's…
Data valuation is an essential task in a data marketplace. It aims at fairly compensating data owners for their contribution. There is increasing recognition in the machine learning community that the Shapley value -- a foundational…
Shapley values originated in cooperative game theory but are extensively used today as a model-agnostic explanation framework to explain predictions made by complex machine learning models in the industry and academia. There are several…
Every weighted tree corresponds naturally to a cooperative game that we call a "tree game"; it assigns to each subset of leaves the sum of the weights of the minimal subtree spanned by those leaves. In the context of phylogenetic trees, the…
The problem of explaining the behavior of deep neural networks has recently gained a lot of attention. While several attribution methods have been proposed, most come without strong theoretical foundations, which raises questions about…
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…
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…
Motivated by the fact that the worth of a coalition may depend on the order in which agents arrive, Nowak and Radzik (1994) (NR) introduced cooperative games with generalized characteristic functions. We study such temporal cooperative…
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…
Shapley values, a game theoretic concept, has been one of the most popular tools for explaining Machine Learning (ML) models in recent years. Unfortunately, the two most common approaches, conditional and marginal, to calculating Shapley…
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…
Artificial Neural Networks have shown impressive success in very different application cases. Choosing a proper network architecture is a critical decision for a network's success, usually done in a manual manner. As a straightforward…
Cooperative interval game is a cooperative game in which every coalition gets assigned some closed real interval. This models uncertainty about how much the members of a coalition get for cooperating together. In this paper we study…
Cooperative game theory studies how to allocate the joint value generated by a set of players. These games are typically analyzed using the characteristic function form with transferable utility, which represents the value attainable by…
The Shapley value (SV) has emerged as a promising method for data valuation. However, computing or estimating the SV is often computationally expensive. To overcome this challenge, Jia et al. (2019) propose an advanced SV estimation…
Measuring contributions is a classical problem in cooperative game theory where the Shapley value is the most well-known solution concept. In this paper, we establish the convergence property of the Shapley value in parametric Bayesian…
Freight forwarding plays a crucial role in facilitating global trade and logistics. However, as the freight forwarding market is extremely fragmented, freight forwarders often face the issue of not being able to fill the available shipping…