preprints.org > computer science and mathematics > applied mathematics > doi: 10.20944/preprints202311.0590.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 8 November 2023 / Approved: 9 November 2023 / Online: 9 November 2023 (07:34:45 CET)

Defining measures of network efficiency and vulnerability for networks is a pivotal aspect in modern networking paradigms. We approach this problem from a game-theoretical perspective. We will consider networks in which actors have social or economic interests modeled by means of a cooperative game. This allows to define, for each network, a family of efficiency measures and another of vulnerability measures, parameterized by the game. The proposed measures use the within groups and the between groups Myerson values. These two values respectively measure which part of the classical allocation of Myerson corresponds to the productivity of players and which part to the intermediation costs. Also, which part of total centrality in social networks is due to communication or to beteewnness. In our proposal, the efficiency of a network is the proportion of the total productivity (or centrality) that players can retain using the network topology. The intermediation costs (and the betweenness centrality) can be viewed as a weakness with a negative impact. Then, we propose to calculate vulnerability as the proportion expent by players in intermediation payments. We explore the properties of these measures and we particularize them to several structures and particular games, also analyzing their asymptotic behaviour.

Game theory; TU-game; Efficiency; Vulnerability, Networks; Communication situation; Myerson value

Computer Science and Mathematics, Applied Mathematics

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