Related papers: Spanning connectivity games
Shapley values, which were originally designed to assign attributions to individual players in coalition games, have become a commonly used approach in explainable machine learning to provide attributions to input features for black-box…
A simple game $(N,v)$ is given by a set $N$ of $n$ players and a partition of $2^N$ into a set $\mathcal{L}$ of losing coalitions $L$ with value $v(L)=0$ that is closed under taking subsets and a set $\mathcal{W}$ of winning coalitions $W$…
Inspired by socio-political scenarios, like dictatorships, in which a minority of people exercise control over a majority of weakly interconnected individuals, we propose vulnerability and power measures defined on groups of actors of…
This paper employs switching-algebraic techniques for the calculation of a fundamental index of voting powers, namely, the total Banzhaf power. This calculation involves two distinct operations: (a) Boolean differencing or differentiation,…
Shapley values are great analytical tools in game theory to measure the importance of a player in a game. Due to their axiomatic and desirable properties such as efficiency, they have become popular for feature importance analysis in data…
This paper generalizes L.S. Shapley's celebrated value allocation theory on coalition games by discovering and applying a fundamental connection between stochastic path integration driven by canonical time-reversible Markov chains and…
This paper defines a general class of cooperative games for which the nucleolus is efficiently computable. This class includes new members for which the complexity of computing their nucleolus was not previously known. We show that when the…
We examine cooperative games where the viability of a coalition is determined by whether or not its members have the ability to communicate amongst themselves independently of non-members. This necessary condition for viability was proposed…
Two straightforward methods to extend an assessment of individual elements to groups are to sum individual assessments or to treat the group as a single merged element and assess it accordingly. In this work, we analyze another natural…
The Shapley-Shubik power index is a measure of each voters power in the passage or failure of a vote. We extend this measure to graphs and consider a discrete-time process in which voters may change their vote based on the outcome of the…
The paper introduces two player connectivity games played on finite bipartite graphs. Algorithms that solve these connectivity games can be used as subroutines for solving M\"uller games. M\"uller games constitute a well established class…
We study the complexity of computing equilibria in two classes of network games based on flows - fractional BGP (Border Gateway Protocol) games and fractional BBC (Bounded Budget Connection) games. BGP is the glue that holds the Internet…
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…
Fractional hedonic games are coalition formation games where a player's utility is determined by the average value they assign to the members of their coalition. These games are a variation of graph hedonic games, which are a class of…
Gvozdeva, Hemaspaandra, and Slinko (2011) have introduced three hierarchies for simple games in order to measure the distance of a given simple game to the class of (roughly) weighted voting games. Their third class $\mathcal{C}_\alpha$…
Oftentimes, the Shapley value becomes infeasible for games with many players. However, establishing symmetry allows for polynomial-time computation. To examine this reduction, we identify the spectrum of homogeneous group games by using an…
In the classical context, the cooperative game theory concept of the Shapley value has been adapted for post hoc explanations of machine learning models. However, this approach does not easily translate to eXplainable Quantum ML (XQML).…
We study strategic games on weighted directed graphs, in which the payoff of a player is defined as the sum of the weights on the edges from players who chose the same strategy, augmented by a fixed non-negative integer bonus for picking a…
The most important challenge in Wireless Sensor Networks (WSNs) is the energy constraint. Numerous solutions have been proposed to alleviate the issue, including clustering. Game theory is an effective decision-making tool that has been…
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,…