Econophysics

Recently the emerging field of econophysics is appearing as a new subdiscipline in physics. Although still in its infancy, the idea is to blend methods of statistical physics, nonlinear dynamics and agent based simulations to problems in the economics realm. In the past, economics has fed from successful physical theories, but now the reverse is happening and a direct interest of the physical community in those subjects has grown. This has been seen in the various conferences organized with both communities.

The field has strongly developed in the areas of financial markets models and social (or economic) collective behaviour, among others. The common features these models posses are a set of agents which 'decide', probably using an evolutionary approach (strategies evolve in time), a set of actions which themselves affect their strategies. Application of the theory of spin glasses and statistical mechanics has been widely applied in order to understand the observed numerical experiments. For a web-page full of bibliography on the subject, please refer to econophysics.org.

Among the collective behaviour modelling, a strong interest is developing in the problem of network formation. These ideas may apply to a market, a society, dispersion of rumors, etc.

A recent contributions from statistical physics to this area has brought new insight into the characterization of social networks. Watts and Strogatz characterized with a simple model networks known as ``small worlds''. These are simply defined as (i) those where the neighborhood of any agent in a social network (for example) looks like if it was a regular lattice (that is, your friends are also friends among them), and (ii) the average distance between any two members of the network scales like logarithm of the size of the network (which is typical for random networks). In other words one can say that small world networks are a mixture of a standart regular lattice (chess board) together with a proportion of ``shortcuts'' which decreases the typical distance between any two points. Examples of this type of networks go from actors databases, to the electric networks, among others.

This opens the question of how such networks can form, and self-organizes in such an optimal way, bringing the best of random and regular networks. This is an example where Statistical Physics has provided new insight into an area of interest in Economics, and an increasing cooperation between both fields would be highly desirable.

References in financial models

	J.-P. Bouchaud, P. Cizeau, L. Laloux and M. Potters: "Mutual attractions: physics and finance", Physics World, January 1999
	R.N. Mantegna and H.E. Stanley: "Scaling Approach to Finance", Cambridge University Press, Cambridge, UK, in press
	L.A.N. Amaral, S.V. Buldyrev, S. Havlin, M.A. Salinger, and H.E. Stanley: "Power Law for a System of Interacting Units with Complex Internal Structure", Phys. Rev. Lett. 80 (1998) 1385-1388

References in network models

	G. Weisbuch, A. Kirman, D. Herreiner, ``Market Organisation'', Santa Fe Institute working paper 95-11-102 (1996).
	D. Watts "Small World: The Dynamics of Networks Between Order and Randomness", Princeton Univ. Press, (1999). D. Watts and S. Strogatz "Collective dynamics of 'small world' networks", Nature 393, 440-442 (1998)
	Agent-Based Computational Economics (ACE) Web Site mantained by Leigh Tesfatsion.
	M. O. Jackson and A. Watts, ``The Evolution of Social and Economic Networks'', Vanderbilt University, Mimeo (1999). See also paper at the Seattle 2000-World Congress of the Econometric Society
	V. Bala and S. Goyal, ``A Non-Cooperative Model of Network Formation'', Econometrica 68, 1181, (2000).
	R. Axelrod, ``The Evolution of Cooperation'', Basic Books, New York (1984)

Subsections

	Dynamics of Cooperation in an Evolving Network
	Self organization in multi-agent models
	Evolving networks models and dispersion of rumors in financial markets