Research group MDEF - Modelli Dinamici in Economia e Finanza (Dynamic Models in Economics and Finance)

Under the auspices of the italian PRIN project:
Interazioni locali e dinamiche globali in economia e finanza: modelli e metodi.
Local interactions and global dynamics in economics and finance: models and tools.

This is an international research network, crated around a group of Italian researchers active since the Eighties of the last century, with the goal of adopting the language and the methodology of the modern qualitative theory of non linear dynamical systems to model and simulate the time evolution of economic, financial and social systems, characterized by complex behaviours and emerging properties resulting from nonlinear interactions, situations of disequilibrium, discontinuities and hysteresis.

We aim at creating a common language and way of working to foster interdisciplinary interaction and collaboration among economists, mathematicians, physicists, ecologists, psychologists etc. interested in dealing with the issues of nonlinearity and complexity (in its many facets) in economic and social systems, as well as in the sustainable management of natural resources, by using geometric, analytic and numerical methods for their global study.

Within fruitful and well-established collaborations among researchers (with heterogeneous backgrounds) taking part in this network, a common goal to various existing research lines is the study of the relationships (and tradeoffs) between ‘local' behaviours (and properties of the subunits of a system) and the ‘global' dynamical properties emerging from their (generally nonlinear) interactions.

As a matter of fact, the study itself of the asymptotic behaviour of a dynamical system consists in deducing the nature of emerging, long-run dynamic patterns, represented by the attractors, from ‘local' laws of motion, which express step-by-step time advancement rules. At the same time, in dynamic models, e.g., of multiple financial markets, industrial districts or networks of marine protected areas, each with its local evolution rules, completely new and often unpredictable dynamic properties can be observed once they are allowed to interact, even weakly, with each other. The onset of emerging properties (and the creation of sometimes surprising structures) is at the basis of evolutionary games and even more apparent in the case of dynamic interactions on graphs (usually called ‘networks' in recent literature).

These are the general topics at the center of collaborations among the researchers involved in this group. Such collaborations produce mathematical models, in the form of nonlinear dynamical systems, which represent the local interactions and time advancement rules (often of adaptive and myopic type); at the same time, mathematical methods are developed for the analysis of the global, or emerging properties that characterize the long-run behaviour of such models.

During the last decades, modern economic theory has witnessed an important shift in methodology. Despite some notable achievements, the standard mainstream approach that describes an economic process as an equilibrium outcome of activities of fully rational and identical economic agents, with the associated paradigm of the representative rational economic agent approach, fails to explain many important features of economic systems, and has been criticized on a number of grounds. At the same time, a growing interest has emerged in alternative approaches which allow for factors such as bounded rationality, heterogeneity, social interaction, and learning. Decisions are not represented as a single (or one-shot) event characterized by full information and full rationality, but the result of an adaptive, or evolutionary process, where sequences of decisions are taken by "trial and error" mechanisms.

In particular, the role played by the heterogeneity of beliefs has become an important topic in the literature and has important implications in explaining how adaptive processes can lead to the emergence of disequilibrium situations observed in economic, financial and social sciences, as well as in the management of bioeconomic systems, characterized by bifurcations and irreversibility. Since the 1990s an alternative approach has been developed where markets are viewed as complex evolving systems, emphasizing non-equilibrium price adjustments through the interaction of many heterogeneous, bounded rational agents. According to this view, aggregate market phenomena are thought of as emerging properties of complex systems, characterized by bifurcations, irreversibility, disequilibrium dynamics. Although complexity in economics, finance and bioeconomics is a relatively new field, a number of important contributions have already been achieved.
Research on complexity in economics, finance and bioeconomics is characterized by an interdisciplinary approach, attracting a number of distinguished scholars from physics, mathematics, computer science, economics, biology, sociology and psychology, and using tools developed in the theory of nonlinear dynamical systems, game theory, optimal control, statistical physics, chaos and bifurcation theory, theory of nonlinear stochastic processes, laboratory experiments with human subjects and agent-based simulation techniques.  With a typical interdisciplinary approach, such methods are generally borrowed from other disciplines where dynamical systems theory represents a common tool of analysis (e.g. mechanics, statistical physics, biology), but often are created ad hoc. In any case, such methods need to be tested on specific applications and compared with the existing results of the economic literature. The group of scholars who participate to this project, and who collaborate with each other since many years, represents an important reference point in Italy with regard to dynamic modelling in economics, finance, and social sciences.
Every two years the University of Urbino hosts the workshop MDEF (Modelli Dinamici in Economia e Finanza).
The participants in this project also collaborate in the organization of the workshop NED (Nonlinear Economic Dynamics), held in Odense ( Denmark ) in 2002 and 2003, in Tokyo in 2004, in Urbino in 2005, in Bielefeld in 2007 and Jönköping (Sweden) in 2009.