Related papers: On Computing the Shapley Value in Bankruptcy Games…
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…
In this paper we investigate the problem of quantifying the contribution of each variable to the satisfying assignments of a Boolean function based on the Shapley value. Our main result is a polynomial-time equivalence between computing…
We show that any cooperative game can be represented by an assignment of costly facilities to players, in which it is intuitively obvious how to allocate the total cost in an equitable manner. This equitable solution turns out to be the…
The Shapley value concept from cooperative game theory has become a popular technique for interpreting ML models, but efficiently estimating these values remains challenging, particularly in the model-agnostic setting. Here, we revisit the…
The Shapley value, originating from cooperative game theory, has been employed to define responsibility measures that quantify the contributions of database facts to obtaining a given query answer. For non-numeric queries, this is done by…
The Shapley value is commonly illustrated by roll call votes in which players support or reject a proposal in sequence. If all sequences are equiprobable, a voter's Shapley value can be interpreted as the probability of being pivotal, i.e.,…
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…
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…
This paper addresses Monte Carlo algorithms for calculating the Shapley-Shubik power index in weighted majority games. First, we analyze a naive Monte Carlo algorithm and discuss the required number of samples. We then propose an efficient…
Shapley value is a concept in cooperative game theory for measuring the contribution of each participant, which was named in honor of Lloyd Shapley. Shapley value has been recently applied in data marketplaces for compensation allocation…
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…
Because of their strong theoretical properties, Shapley values have become very popular as a way to explain predictions made by black box models. Unfortuately, most existing techniques to compute Shapley values are computationally very…
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…
The Shapley value was originally introduced in cooperative game theory as a wealth distribution mechanism. It has since found use in knowledge representation and databases for the purpose of assigning scores to formulas and database tuples…
Weighted voting games are a well-known and useful class of succinctly representable simple games that have many real-world applications, e.g., to model collective decision-making in legislative bodies or shareholder voting. Among the…
For $f$ a weighted voting scheme used by $n$ voters to choose between two candidates, the $n$ \emph{Shapley-Shubik Indices} (or {\em Shapley values}) of $f$ provide a measure of how much control each voter can exert over the overall outcome…
As data emerges as a vital driver of technological and economic advancements, a key challenge is accurately quantifying its value in algorithmic decision-making. The Shapley value, a well-established concept from cooperative game theory,…
Reinforcement learning has achieved remarkable success in complex decision-making environments, yet its lack of transparency limits its deployment in practice, especially in safety-critical settings. Shapley values from cooperative game…
As the complexity of software systems rises, methods for explaining their behaviour are becoming ever-more important. When a system fails, it is critical to determine which of its components are responsible for this failure. Within the…
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,…