Strategic Connections in a Hierarchical Society: Wedge Between Observed and Fundamental Valuations

In an interconnected society, social networks grow through formation of strategic connections based on the hierarchy within the social network. Often, the hierarchy becomes self-reinforcing and the observed valuations of the individuals in the hierarchy become disconnected from the corresponding fundamentals. We propose a network model to characterize the disconnect between the observed and fundamental valuations of entities, where the difference is a function of the linkages across the entities. In a growing social network, new entrants come at every point of time and offer connections to the incumbents based on the observed valuations. Individuals care only about their ranks in the hierarchy of observed valuation. With myopic individuals, network grows in equilibrium, but the associated hierarchy becomes unstable. However, with farsighted individuals, the network growth process is hierarchy-preserving and depending on the structure of seed network, the process may be completely halted by individuals who have incentives to preserve hierarchy. These two mechanisms taken together provide a comprehensive characterization of valuation in a growing inter-connected, hierarchical society. We illustrate an application of the model by analyzing the Indian board interlocking network. Our model enables us to find the hierarchy of the board members’ network and to identify the dispersion in magnitude of network externalities across directors.