Efficiency and Vulnerability in Networks: A Game Theoretical Approach

Abstract

Defining measures of network efficiency and vulnerability is a pivotal aspect of modern networking paradigms. We approach this issue from a game theoretical perspective, considering networks where actors have social or economic interests modeled through a cooperative game. This allows us 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 values, respectively, measure the portion of the classical Myerson allocation corresponding to the productivity of players and the part related to intermediation costs. Additionally, they indicate the portion of total centrality in social networks attributed to communication or betweenness. In our proposal, the efficiency of a network is the proportion of total productivity (or centrality) that players can retain using the network topology. Intermediation costs (and betweenness centrality) can be seen as a weakness with a negative impact. Therefore, we suggest calculating vulnerability as the proportion of expenses players incur in intermediation payments. We explore the properties of these measures and tailor them to various structures and specific games, also analyzing their asymptotic behavior.