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Scientific Report 2007-2009
Condensed matter physics and biophysics
C12. Complex agents in the global network: selforganization and
instabilities
The science of complex systems
The study of complex systems refers to the emergency
of collective properties in systems with a large number
of parts in interaction among them. These elements can
be atoms or macromolecules in a physical or biological
context, but also people, machines or companies in a
socio-economic context. The science of complexity tries
to discover the nature of the emerging behavior of complex
systems, often invisible to the traditional approach,
by focusing on the structure of the interconnections and
the general architecture of systems, rather than on the
individual components. For a general overview see Ref
(1) and for all our activities the WEB page below.
The science of complexity arises naturally from statistical
mechanics which, in the seventies, introduces a
fundamental change of paradigm with respect to the reductionist
scientific vision. At the equilibrium point between
order and disorder one can observe fluctuations
at all scales and the system cannot be described any
more with the usual formalism in which one tries to write
simple equations for average quantities. From this conceptual
grain many new concepts have developed which
produced a revolution in our way of looking at nature:
scaling laws, renormalization group, fractal geometry,
glassy and granular systems, complex liquids, colloids
and many others. Also the understanding of Superconductivity
as an emergent collective effect associated with
symmetry breaking has been a very important element in
the development of these ideas. An important implication
of these ideas is about the complex properties of the
large scale cosmic structures. This will probably lead to
a major revision of the standard model of cosmology with
deep implications on dark matter and dark energy (2).
More recently it begins to be clear that these concepts
can have much broader applications with respect to the
physical systems from which they originated. This led
to a large number of interdisciplinary applications which
are sometimes surprising and which probably represent
just the beginning of the many 7possible applications.
From Physics to Finance and Economics
After the sub-prime crisis in the financial world there
have been many conjectures for the possible origin of this
instability. Most suggestions focus on concepts like collective
behavior, contagion, network domino effect, coherent
portfolios, lack of trust, liquidity crisis, and, in
general psychological components in the traders behavior
(3). These properties are usually neglected in the
standard risk analysis which is based on a linear analysis
within a cause-effect relation. These new concepts
require a novel approach to the risk problem which could
profit from the general ideas of complex systems theory.
This corresponds to the introduction of suitable models
with heterogeneous agents and a different perspective
in which the interaction between agents (direct or
in direct) is explicitly considered together with the idea
that the system may become globally unstable in the
sense of self-organized criticality. The analysis is therefore
shifted from the cause-effect relation to the study of
the possible intrinsic instabilities. Our research project
corresponds to a systematic analysis of these ideas based
on agent models and order book models (4) together with
the statistical analysis of experimental data. The final
objective of these studies would be to define the characteristic
properties of each of the above concepts from the
models and then to identify their role and importance in
the real financial markets.
Number of active agents
10000
1000
100
N 1
N 2
10
0 1e+06 2e+06 3e+06 4e+06 5e+06
Time
Figure 1: Self-organization towards the quasi-critical state of
the market. Different populations of agents with a different
starting number (3000 for the green line; 500 for the red and
50 the blue) evolve spontaneously and self-organize towards
a state with an effective number of agents corresponding to
the intermittent behavior with non-Gaussian properties. The
state which is the attractor of the dynamics corresponds to
the stylized facts observed in real markets.
References
1. L. Pietronero, Europhys. News 39 p. 26 (2008)
2. S. Weinberg, Cosmology, Oxford Univ. Press (2008).
3. V.Alfi et al., Europhys. Lett. 86 58003, 2009.
4. V. Alfi, et al., Nature Physics 3, 746 (2007).
Authors
V. Pietronero, V. Alfi, M. Cristelli, A. Zaccaria
http://pil.phys.uniroma1.it/twiki/bin/view
/Pil/WebHome
N*
Sapienza Università di Roma 65 Dipartimento di Fisica