Modelling social capital: the structural hole connections game

Social Capital is considered as the value that an actor draws from the network. It is measured as an ability to bond with others (bonding capital) as well as an ability to form a bridge that connects otherwise disconnected actors or groups in the network (bridging capital). In order to model the social capital, the strategic nature of forming links needs to be considered and baked within the network formation models. In this paper, we develop a strategic network formation game named Structural Hole Connections Game (shc) and define an associated allocation function that distributes the total network value to the actors in the network in such a way that captures their bonding and bridging social capital. Our proposed shc game generalizes the utility function that models both the bonding and bridging capabilities of an actor with high social capital. We first analytically deduct the efficient and stable networks of the shc game. Finally, we analyse a real-world social network of employees of an IT company and identify individuals with binding and bridging social profiles.