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Game-theoretic Network Centrality: A Review
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This work reviews the main game-theoretic network centrality measures from both bodies of literature and organizes them into two categories: those that are more focused on the connectivity of nodes, and those that is morefocused on the synergies achieved by nodes in groups.Abstract:
Game-theoretic centrality is a flexible and sophisticated approach to identify the most important nodes in a network. It builds upon the methods from cooperative game theory and network theory. The key idea is to treat nodes as players in a cooperative game, where the value of each coalition is determined by certain graph-theoretic properties. Using solution concepts from cooperative game theory, it is then possible to measure how responsible each node is for the worth of the network.
The literature on the topic is already quite large, and is scattered among game-theoretic and computer science venues. We review the main game-theoretic network centrality measures from both bodies of literature and organize them into two categories: those that are more focused on the connectivity of nodes, and those that are more focused on the synergies achieved by nodes in groups. We present and explain each centrality, with a focus on algorithms and complexity.read more
Citations
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Centrality and power in social networks: A game theoretic approach
Daniel Gómez González,Enrique González Arangüena,Conrado Miguel Manuel García,Guillermo Owen,Juan Antonio Tejada Cazorla +4 more
TL;DR: A new family of centrality measures, based on game theoretical concepts, is proposed for social networks to reflect the interests that motivate the interactions among individuals in a network, and the graph-restricted game is obtained.
Journal ArticleDOI
Tournament solutions based on cooperative game theory
TL;DR: This work applies solution concepts developed for simple games and considers the desirability relation and the power indices which preserve this relation to the case of weak tournaments and shows that each minimal winning coalition consists of a certain uncovered candidate and its dominators.
Proceedings ArticleDOI
Responsibility and verification: importance value in temporal logics
TL;DR: In this paper, the importance of a component is measured by giving its control to an adversary, alone or along with other components, and testing whether the system can still fulfill the specification, and several ways to transpose it to branching ones.
Journal ArticleDOI
Using the Shapley Value to Mitigate the Emergency Rescue Risk for Hazardous Materials
TL;DR: This paper proposes a gradual-coverage game describing the situation of locating emergency facilities, to which the Shapley value can be used to evaluate the candidate locations, and characterize the Shapleys value by proposing two new axioms.
Posted Content
Maximizing Influence-based Group Shapley Centrality
TL;DR: Strong hardness of approximation results are obtained for the influence maximization problem, where it is shown that a greedy algorithm can achieve a factor of 1-1/e-\epsilon for any $k>0, showing that not all is lost in settings where $k$ is bounded.
References
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Journal ArticleDOI
Centrality in social networks conceptual clarification
TL;DR: In this article, three distinct intuitive notions of centrality are uncovered and existing measures are refined to embody these conceptions, and the implications of these measures for the experimental study of small groups are examined.
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Factoring and weighting approaches to status scores and clique identification
TL;DR: In this paper, Factoring and weighting approaches to status scores and clique identification were proposed, and the results showed that the weighting approach is more accurate than the factoring approach.
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Cores of Convex Games
TL;DR: In this article, it was shown that the core of a convex game is not empty and that it has an especially regular structure, and that certain other cooperative solution concepts are related in a simple way to the core.
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Graphs and Cooperation in Games
TL;DR: Graph-theoretic ideas are used to analyze cooperation structures in games, and fair allocation rules are proven to be unique, closely related to the Shapley value, and stable for a wide class of games.