Centrality in directed social networks. A game theoretic approach

Pozo, Mónical Del; Manuel, Conrado; González–Arangüena, Enrique; Owen, Guillermo

doi:10.1016/j.socnet.2011.04.001

Cited by 45 publications

(14 citation statements)

References 35 publications

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“…The collection K of all sharing systems k 2 K on N is defined by Hammer et al (1977) andVasil'ev (1978), independently of each other, defined a class of TU-values. While Hammer et al (1977) and, e. g., Derks et al (2000) this class call selectope 2 , Vasil'ev (1978), Vasil'ev and van der Laan (2002), and, e. g., del Pozo et al (2011 refer to this class as Harsanyi set, abbreviated to H. For all N 2 N ; ðN; vÞ 2 V N , and each sharing system k 2 K, the Harsanyi solution H k 2 H assigns to any (N, v) a vector in R N defined as…”

Section: Tu-gamesmentioning

confidence: 99%

Harsanyi support levels solutions

Besner

2021

Theory Decis

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We introduce a new class of values for TU-games (games with transferable utility) with a level structure, called LS-games. A level structure is a hierarchical structure where each level corresponds to a partition of the player set, which becomes increasingly coarse from the trivial partition containing only singletons to the partition containing only the grand coalition. The new values, called Harsanyi support levels solutions, extend the Harsanyi solutions for LS-games. As an important subset of the class of these values, we present the class of weighted Shapley support levels values as a further result. The values from this class extend the weighted Shapley values for LS-games and contain the Shapley levels value as a special case. Axiomatizations of the studied classes are provided.

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Section: Tu-gamesmentioning

confidence: 99%

Harsanyi support levels solutions

Besner

2021

Theory Decis

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“…Finally, a number of authors considered game-theoretic centralities for directed graphs (Gomez et al, 2003;del Pozo et al, 2011). However, no axiomatization has been proposed for any such centrality measure.…”

Section: Game-theoretic Network Centralities Not Requiring Connectivitymentioning

confidence: 99%

“…One family of centralities that has recently attracted growing attention is based on Cooperative, or "Coalitional", Game Theory (Gomez, González-Arangüena, Manuel, Owen, del Pozo, & Tejada, 2003;del Pozo, Manuel, González-Arangüena, & Owen, 2011;Michalak, Aadithya, Szczepański, Ravindran, & Jennings, 2013;Szczepański, Michalak, & Rahwan, 2016). Here, the key idea is to analyse the topology of the network using the combinatorial structure of a coalitional game.…”

Section: Introductionmentioning

confidence: 99%

Axiomatic Characterization of Game-Theoretic Centrality

Skibski

Michalak

Rahwan³

2018

jair

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One of the fundamental research challenges in network science is centrality analysis, i.e., identifying the nodes that play the most important roles in the network. In this article, we focus on the game-theoretic approach to centrality analysis. While various centrality indices have been recently proposed based on this approach, it is still unknown how general is the game-theoretic approach to centrality and what distinguishes some game-theoretic centralities from others. In this article, we attempt to answer this question by providing the first axiomatic characterization of game-theoretic centralities. Specifically, we show that every possible centrality measure can be obtained following the game-theoretic approach. Furthermore, we study three natural classes of game-theoretic centrality, and prove that they can be characterized by certain intuitive properties pertaining to the well-known notion of Fairness due to Myerson.

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“…However, other power measures from the literature can be applied, such as the ones given by Gould [15], White and Borgatti [16], the β-measure of van den Brink and Gilles [17] and its reflexive version in van den Brink and Borm [18], the λ-measure of Borm et al [19], the positional power measure of Herings et al [20] or the centrality measures in del Pozo et al [21]. This also shows how social network theory and mathematical game theory are intertwined as soon as we consider network structures among players in a game.…”

Section: Introductionmentioning

confidence: 99%

Power Measures and Solutions for Games Under Precedence Constraints

Algaba

Brink

Dietz

2017

J Optim Theory Appl

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Games under precedence constraints model situations, where players in a cooperative transferable utility game belong to some hierarchical structure, which is represented by an acyclic digraph (partial order). In this paper, we introduce the class of precedence power solutions for games under precedence constraints. These solutions are obtained by allocating the dividends in the game proportional to some power measure for acyclic digraphs. We show that all these solutions satisfy the desirable axiom of irrelevant player independence, which establishes that the payoffs assigned to relevant players are not affected by the presence of irrelevant players. We axiomatize these precedence power solutions using irrelevant player independence and an axiom that uses a digraph power measure. We give special attention to the hierarchical solution, which applies the hierarchical measure. We argue how this solution is related to the known precedence Shapley value, which does not satisfy irrelevant player independence, and thus is not a precedence power solution. We also axiomatize the hierarchical measure as a digraph power measure.

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Centrality in directed social networks. A game theoretic approach

Cited by 45 publications

References 35 publications

Harsanyi support levels solutions

Harsanyi support levels solutions

Axiomatic Characterization of Game-Theoretic Centrality

Power Measures and Solutions for Games Under Precedence Constraints

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