An Analytical Solution for Agent Based Models 

C. Di Guilmi†(1), M. Gallegati (2), S. Landini(3), and J. E. Stiglitz (4) 

1 School of Finance  and Economics,  University  of Technology,  Sydney, Australia.

2 Department of Economics,  Universita` Politecnica delle Marche,  Italy

3IRES  Piemonte, Turin, Italy

4 Columbia University,  New York, USA

Presenter: Professor Mauro Gallegati
                    Department of Economics and Social Sciences
         Polytechnic University of Marche.

Abstract

One of the consequences of the failure of mainstream theory in convincingly taking into account the heterogeneity of agents is the misrepresentation of markets with asymmetric information. In fact, the consideration of players with diverse information sets is at odd with the idea of the representative agent. The Global Financial Crisis spectacularly exposed this inconsistency, casting doubts on the core neoclassical assumptions for the representation of markets. Moreover, standard modelling techniques leave no or little room for agents inter- action, which is the most intriguing and relevant corollary of the het- erogeneity. In this paper we propose a model with heterogeneous and interacting firms and banks, which is solved analytically. Methodologically, the economy is modelled as a network, a theoretical structure which is particularly suitable to represent the interactions among different individuals. In this credit network firms interact directly with banks and, indirectly, among themselves. The main novelty is the use of the master equation to perform the aggregation over a population of heterogeneous firms and to describe the endogenous evolution of the network. The asymptotic solution of the master equation provides a system of coupled equations, governing the dynamics of growth and fluctuations of the aggregate output and the network degree. Keywords: heterogeneity, financial fragility, master equation, interaction, dynamic aggregation.