Related papers: Shapley Values in Weighted Voting Games with Rando…

This paper concerns the analysis of the Shapley value in matching games. Matching games constitute a fundamental class of cooperative games which help understand and model auctions and assignments. In a matching game, the value of a…

Power indices are essential in assessing the contribution and influence of individual agents in multi-agent systems, providing crucial insights into collaborative dynamics and decision-making processes. While invaluable, traditional…

Changes in input distribution can induce shifts in the average predictions of machine learning models. Such prediction shifts may impact downstream business outcomes (e.g. a bank's loan approval rate), so understanding their causes can be…

In allocation problems, a given set of goods are assigned to agents in such a way that the social welfare is maximised, that is, the largest possible global worth is achieved. When goods are indivisible, it is possible to use money…

We propose a novel definition of Shapley values with uncertain value functions based on first principles using probability theory. Such uncertain value functions can arise in the context of explainable machine learning as a result of…

This paper makes the case for using Shapley value to quantify the importance of random input variables to a function. Alternatives based on the ANOVA decomposition can run into conceptual and computational problems when the input variables…

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…

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…

This paper is a twofold contribution. First, it contributes to the problem of enumerating some classes of simple games and in particular provides the number of weighted games with minimum and the number of weighted games for the dual class…

A large branch of explainable machine learning is grounded in cooperative game theory. However, research indicates that game-theoretic explanations may mislead or be hard to interpret. We argue that often there is a critical mismatch…

Originating in game theory, Shapley values are widely used for explaining a machine learning model's prediction by quantifying the contribution of each feature's value to the prediction. This requires a scalar prediction as in binary…

Shapley value has recently become a popular way to explain the predictions of complex and simple machine learning models. This paper is discusses the factors that influence Shapley value. In particular, we explore the relationship between…

Important decisions are likely made by groups of agents. Thus group decision making is very common in practice. Very transparent group aggregating rules are given by weighted voting, where each agent is assigned a weight. Here a proposal is…

In this paper, we study the problem of learning the skill distribution of a population of agents from observations of pairwise games in a tournament. These games are played among randomly drawn agents from the population. The agents in our…

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…

The Shapley value is the solution concept in cooperative game theory that is most used in both theoretical as practical settings. Unfortunately, computing the Shapley value is computationally intractable in general. This paper focuses on…

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…

Weighted voting games are a family of cooperative games, typically used to model voting situations where a number of agents (players) vote against or for a proposal. In such games, a proposal is accepted if an appropriately weighted sum of…

Coalitional voting games appear in different forms in multi-agent systems, social choice and threshold logic. In this paper, the complexity of comparison of influence between players in coalitional voting games is characterized. The…

The Shapley effects are global sensitivity indices: they quantify the impact of each input variable on the output variable in a model. In this work, we suggest new estimators of these sensitivity indices. When the input distribution is…