Related papers: Power measures derived from the sequential query p…

In cooperative game theory, associated games allow for providing meaningful characterizations of solution concepts. Moreover, generalized values allow computing an influence or power index of each coalition in a game. In this paper, we view…

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…

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…

This paper establishes a complete theoretical foundation for the Hodge-theoretic extension of the Shapley value introduced by Stern and Tettenhorst (2019). We show that a set of five axioms--efficiency, linearity, symmetry, a modified…

We introduce the prediction value (PV) as a measure of players' informational importance in probabilistic TU games. The latter combine a standard TU game and a probability distribution over the set of coalitions. Player $i$'s prediction…

Following the original interpretation of the Shapley value (Shapley, 1953a) as a priori evaluation of the prospects of a player in a multi-person interaction situation, we propose a group value, which we call the Shapley group value, as a…

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…

We investigate a class of weighted voting games for which weights are randomly distributed over the standard probability simplex. We provide close-formed formulae for the expectation and density of the distribution of weight of the $k$-th…

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…

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…

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…

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…

We study a game first introduced by Martin (actually we use a slight variation of this game) which plays a role for measure analogous to the Banach-Mazur game for category. We first present proofs for the basic connections between this game…

Matching games naturally generalize assignment games, a well-known class of cooperative games. Interest in matching games has grown recently due to some breakthrough results and new applications. This state-of-the-art survey provides an…

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…

The classic paper of Shapley and Shubik \cite{Shapley1971assignment} characterized the core of the assignment game using ideas from matching theory and LP-duality theory and their highly non-trivial interplay. Whereas the core of this game…

When the performance of a team of agents exceeds our expectations or fall short of them, we often explain this by saying that there was some synergy in the team---either positive (the team exceeded our expectations) or negative (they fell…

We revisit the crucial issue of natural game equivalences, and semantics of game logics based on these. We present reasons for investigating finer concepts of game equivalence than equality of standard powers, though staying short of modal…

The sequential equilibrium is a standard solution concept for extensive-form games with imperfect information that includes an explicit representation of the players' beliefs. An assessment consisting of a strategy and a belief is a…

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…