Dynamic Aggregation of Heterogeneous Interacting Agents and Network: An Analytical Solution for Agent Based Models

One of the consequences of the failure of mainstream theory in convincingly taking into account the heterogeneity of agents and their interaction is the misrepresentation of markets with asymmetric information. This paper presents a credit network model with heterogeneous firms and banks which is solved analytically. The solution is articulated in two steps which involve two different master equations. The first performs the aggregation over a population of firms that are heterogeneous in size and financial conditions in order to identify the number of firms that enter the credit market. The second master equation uses the solution of the first to describe the dynamic evolution of the network structure and in particular of the network degree. The analytical solution provides a system of equations that generates the same outcomes of the numerical solution and can provide some insights on the causal relationships governing the dynamics of boom and bust in the economy as a consequence of the evolution of the concentration in the credit market.