The Evolution and Emergence of Integrated Social and Financial Networks with Electronic Transactions: A Dynamic Supernetwork Theory for the Modeling, Analysis, and Computation of Financial Flows and Relationship Levels

In this paper, we propose a rigorous dynamic supernetwork theory for the integration of social networks with financial networks with intermediation in the presence of electronic transactions. We consider decision-makers with sources of funds, financial intermediaries, as well as demand markets for the various financial products. Through a multilevel supernetwork framework consisting of the financial network and the social network we model the multicriteria decision-making behavior of the various decision-makers, which includes the maximization of net return, the maximization of relationship values, and the minimization of risk. Increasing relationship levels in our framework are assumed to reduce transaction costs as well as risk and to have some additional value for the decision-makers. We explore the dynamic evolution of the financial flows, the associated product prices, as well as the relationship levels on the supernetwork until an equilibrium pattern is achieved. We provide some qualitative properties of the dynamic trajectories, under suitable assumptions, and propose a discrete-time algorithm which is then applied to track the evolution of the relationship levels over time as well as the financial flows and prices. The equilibrium pattern yields, as a byproduct, the emergent structure of the social and financial networks since it identifies not only which pairs of nodes will have flows but also the size of the flows, i.e., the relationship levels and the financial transactions.