Accessibility in oriented networks

Ramon, Rafael Amer; Giménez, José Miguel; Magaña, Antonio

doi:10.1016/j.ejor.2006.04.027

Cited by 10 publications

(10 citation statements)

References 13 publications

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“…Moreover, approximation techniques have not yet been developed for many solution concepts or for game-theoretic network centrality measures that are inspired by Myerson's graph-restricted games. In particular, the work by [1,2] seems well suited for this.…”

Section: Discussionmentioning

confidence: 99%

Monte Carlo Techniques for Approximating the Myerson Value -- Theoretical and Empirical Analysis

Tarkowski,

Matejczyk,

Michalak

et al. 2020

Preprint

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Myerson [16] first introduced graph-restricted games in order to model the interaction of cooperative players with an underlying communication network. A dedicated solution concept-the Myerson value-is perhaps the most important normative solution concept for cooperative games on graphs. Unfortunately, its computation is computationally challenging. In particular, although exact algorithms have been proposed [20], they must traverse all connected coalitions of the graph of which there may be exponentially many.In this paper, we consider the issue of approximating the Myerson value for arbitrary graphs and characteristic functions. While Monte Carlo approximations have been proposed for the related concept of the Shapley value [3,6,10], their suitability for the Myerson value has not been studied. Given this, we evaluate and compare (both theoretically and empiraclly) three Monte Carlo sampling methods for the Myerson value: conventional method of sampling permutations; a new, hybrid algorithm that combines exact computations and sampling; and sampling of connected coalitions. We find that our hybrid algorithm performs very well and also significantly improves on the conventional methods.

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Section: Discussionmentioning

confidence: 99%

Monte Carlo Techniques for Approximating the Myerson Value -- Theoretical and Empirical Analysis

Tarkowski,

Matejczyk,

Michalak

et al. 2020

Preprint

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“…Section 4.3 presents the centrality due to del Pozo et al ( 2011) for digraphs. The centralities due to Amer et al (2007) and Belau (2014) then follow in Sections 4.4 and 4.5, respectively. Section 4.6 discusses the Banzhaf network centrality, proposed by Grofman and Owen (1982), which shares certain (but not all) traits with the connectivity approach.…”

Section: Game-theoretic Node Centrality Measures Based On Connectivitymentioning

confidence: 94%

“…In the next section, we move on to a measure of centrality developed by Amer et al (2007). Although the centrality presented in this section stems from the work by Gómez et al (2003), which makes prominent use of the Myerson value, it is not in fact based on the idea of graph-restricted games according to Myerson.…”

Section: The Myerson Value As a Centrality Measurementioning

confidence: 99%

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Game-theoretic Network Centrality: A Review

Tarkowski¹,

Michalak²,

Rahwan³

et al. 2018

Preprint

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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 gametheoretic 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.

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“…Remark 2.7 For a given digraph without a predefined game, we can consider different test games, which allow us to modulate accessibility according to the game definition. The test games, chosen among the symmetric games, were introduced in Amer et al [1], where, in addition, we can find applications of this procedure to several particular situations described by means of directed graphs.…”

Section: Definition 21mentioning

confidence: 99%

A ranking for the nodes of directed graphs based on game theory (Poster Presentation)

Ramon

Giménez

Magaña

2007

Proc Appl Math and Mech

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We introduce a value that allows us to emphasize the importance of each player in a cooperative game when the cooperation possibilities are limited according to the links of an oriented network. The proposed concept of accessibility tries to conjugate the marginal contributions of each node as a game player with the cooperation geometry imposed by the directed graph that models the network. As a consequence, it is possible to offer a ranking for the nodes of directed graphs.

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Accessibility in oriented networks

Cited by 10 publications

References 13 publications

Monte Carlo Techniques for Approximating the Myerson Value -- Theoretical and Empirical Analysis

Monte Carlo Techniques for Approximating the Myerson Value -- Theoretical and Empirical Analysis

Game-theoretic Network Centrality: A Review

A ranking for the nodes of directed graphs based on game theory (Poster Presentation)

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