Workshop CNRS-NSFC on

Paris
- 20 to 22 of September 2001

** **

*Organised by GREQAM - Marseille and CREA - Paris*

*Under the auspices of CNRS and NSFC*

** **

** **

**Chinese participants:**

Ø
**Professor CHENG Siwei**

Director General of the Department
of Management Sciences

National Natural Science Foundation
of China

Vice Chairman of the National
People’s Congress, P. R. China

**"Some Prospects
of the Complexity Science "**

Ø
**Professor Dr. CHEN Ping**

China Center for Economy Research

Peking University

**Economic Complexity:
The Origin of Division of Labor and**

**Persistent Business
Cycles**

Adam Smith once observed that division of labor
was limited by the extent of the market. Monopolistic powers were resulted from
a limited market. However, Smith also believed that a competitive market was
guided by invisible hands. George Stigler noted that Smith’s two theories were
not compatible with each other. The persistent nature of business cycles cannot
be explained by equilibrium models, such as the Frisch model of a noise-driven
oscillator and the Lucas model of micro fluctuations under rational
expectations.

We
introduce resource expansion and risk taking in market competition. The
division of labor is limited by the market extent, resource variety, and environment
uncertainty. The Stigler dilemma can be solved by the trade-off between
stability and complexity in economic systems. Persistent business cycles are
better described by nonlinear trends and color chaos in two-dimensional
time-frequency Gabor space. Cultural diversity and economic resilience can be
understood from the perspective of self-organization under nonlinear
interactions and non-equilibrium constraints.

JEL
Classification: L10, E32, C52, B22, B23

Key Words: Division of labor,
Persistent business cycles, Economic organisms, Complex dynamics

Ø
**Professor DAI Ruwei**

Institute of Automation

The Chinese Academy of Sciences

Hall for Workshop of Metasynthetic Engineering

Abstract: In this article,
first we make a comparison between autonomous intelligent systems with
man-computer synergetic intelligent systems, then discuss such two kinds of
systems from point view of complexity. Actually, the man-computer synergetic
intelligent system belongs to the category of open complex giant systems. We
briefly introduce such systems and the methodology of open complex giant
systems – Metasynthesis from qualitative to quantitative. In addition, the hall
for workshop of metasynthetic engineering which is an expanded form of
metasynthesis, is also discussed.

Key Words**:** metasynthesis,
man-computer cooperated system, complexity

Ø
**Professor Dr. HUANG Dengshi**

School of Economics and Management

Southwest Jiaotong University

**Microeconomic Mechanisms
of Density Cycle in Cournot Duopoly**

Abstract: When the
reaction function is unimodal, Kopel (1996), Dana and Montrucchio (1986), Puu
(1991) and Bischi (2000) all studied about the cyclical and chaotic states of
Cournot model. Such results are all concerned about the complex behaviors of
Cournot model without random disturbance, so the complexity occurs in a certain
system. Applying such conclusions to economic practice requires actually
measuring the quantities of two firms or at least obtaining the actual
beginning quantities. Otherwise the application is impossible. But in reality,
we can not obtain the accurate quantity and only know the distributions of the
beginning quantities. Now the problem is how the density evolves in Cournot
model. If we can make sure the evolution of density in Cournot model, we can
forecast the quantity in probability and study the evolution of economic system
by combining the randomness and certainty.

The conclusions of
theoretical researches and computer experiments show that as long as the period
of evolution is long enough, the density could evolve to the stable, cyclic,
chaotic or more complex states. In economic system the cyclic state is maybe
the most important state (the stable is a particular case of the cyclic),
sometimes the cyclical state is called density cycle. The density cycle is a very
important characteristic in economic system. Even when the economic system is
stable, such stability is about the density not about the total. And the
density cycle of economic system is the cycling of the density not the total.
For example, in duopoly, the total quantity can be increasing, but in every
period, the ratio of the quantity of one firm to the total can be cyclical.
From a view of nonlinear science, an economic system can be other states except
for the density cycle (the density stability is a particular case). But from a
view of economic theory and practice, the density cycle is important. It is
well known that the economic phenomena are cyclical, but until now there is no
theories can explain the cycling of economic phenomena completely. The theory
of density cycle can contribute to it. Huang Dengshi et al.(1997)^{ }concerned
about the density cycle in duopoly but not involving the economic signification
and micro-mechanism of unimodal reaction function.

In this paper, the
microeconomic mechanisms of density cycle in Cournot duopoly are studied. The quantitative
description for the density cycle is introduced and these general results are
applied to the study of the economic complexity in Counot duopoly. Economic signification
of the density cycle in Cournot duopoly is analyzed in detail. The directions
for further research in this field are presented at the end of the paper.

Key words: Cournot Duopoly; Economic Complexity; Density Cycle

Ø **Professor Dr. LI
Yuanxiang**

State Key Laboratory of Software
Engineering

Wuhan University

**Evolutionary modeling
and computing for complex systems**

Abstract: In this
presentation, we will introduce some basic principles for evolutionary
computations and a general framework for designing evolutionary algorithms.
Some theoretical bases related to other disciplines are briefly discussed. Then
we will focus on some applications of evolutionary computations for complex
system modeling. Firstly, model-building for differential equations is
presented by using evolutionary algorithms. In practice, some systems are
described as differential equations, for example, a time series is often
described by using an ordinary equation. Secondly, a classifier system is
designed by combined with evolutionary algorithms which are used to learn rules
of the classifier from practical data. Thirdly, evolvable hardware (EHW)
technology is introduced. The EHW is combined the evolutionary computation with
the technology of electronic design automation (EDA), and it will develop a new
generation of EDA technology. These applications will show the universality,
intelligence and parallelism, which are outstanding features of evolutionary
computations.

Ø **Professor Dr. LIU
Hong**

School of Business

Nanjing University

Abstract: A collection of
interdisciplinary scientific efforts on link of complexity science and
management sciences are emerging, and part of the efforts is associated chaos
theory with business administration. With the extraordinary growth of interest
in such efforts, however, there are still doubts such as “complexity theory in
organization science: seizing the promise or becoming a Fad?” Because author
encountered similar question 10 years ago when he began to learn chaos theory
and tried to combine it to management, thereby, he firstly argues the bases of
such efforts, then proposes the two disciplines conjunctive points which include using chaos theory explaining management
behaviors and business phenomena, revealing chaos exists in management systems
and allowing for new insights into enterprise management. Author reviews
results obtained by applying chaos theory in researching business
administration, which are mainly concerned with such links as chaos and
fundamental characteristics of enterprise system, chaos and planning, chaos and
forecasting, chaos and organizing, chaos and controlling, and chaos and
strategy. Besides above themes, author argues that there is many management
fields else should be linked to chaos theory and the effort would be meaningful
for researchers to pay attention to because their deeper insights have not been
researched. Author claims that an organization life cycle can be treated as an
evolution of nonlinear interaction between internal elements and outside
environment so that we can apply chaos theory researching organization
development and change. Chaos theory and other complexity theory could be
applying to research forecasting methodologies and find out new forecasting or
predicting paradigms. According to chaotic system theory, new method of
organization could be designed in order that the organization can adapt complex
and rapidly changing environment. Author points out some difficulties that
would be encountered. In the final, author puts up with some further research
interests, which include:

Applying chaos to research organizational management and development,
which involves organizational plan, control, motivation, strategy, culture,
changes and organizational evolution rules.

According to complexity science, researching how to enable an
organization becoming a complex adaptive system (CAS) and self-organization,
which involves attractor, attractor basin, state space, patterns of
organization and organizational design.

Researching behaviors of multi-agent organization network-based,
especially associating with human resource management, which involves
communication complexity, relationship between local and integral performance,
management policies for complex organization’s survival and vitality, chaos
paradigms whether and to what extend could influence enterprise behavior.

For using complexity science research tool such as swarm-tool-kit,
defining some fundamental concepts such as agent description, relationship
among agents as to given problem.

Key words Complexity science, Chaos theory,
Enterprise, Chaos management, System Theory

Ø
**Professor MA Yuanye**

Kunming Institute of Zoology, CAS

**From Neuron To Mind**

**-----The Complex
System of the Primates’ Brain**

** **

ABSTRACT The information process of primates brain is
discussed as a complex system. The complexity of the primates brain results
from consciousness and mental activity that causes the brain to be even more
complex. The visual information process is used as an example to discuss the
diversity and complexity of the primates’ brain. Also the significance of the
prefrontal body-referenced spatial process is emphasized to be the source of
the self-recognition.

Key Words:
Complex System ; Information Process ;Primates Higher brain
function

Ø
**Professor Dr. SONG Xuefeng, **

Dean School of Management

China University of Mining &
Technology

**THE COMPLEXITY IN
STOCK MARKETS**

ABSTRACT: At present most
researches on the chaotic fluctuant law of stock market are restricted in
seeking the proof that chaos exists in stock markets. But nothing has been done
on the difference between the chaotic statuses of different countries and the
causes. That might relate to the high complexity of chaotic economic system so
that any simple variable cannot explain its complexity and irregularity well.
Song (1996) put forward the degree of chaos for analyzing stock market, and it’s
a bridge across the chaotic phenomenon and the realistic economic change.
Meanwhile chaotic degree can portray quantitatively the complexity and
irregularity of systems.

In this paper, we utilize the chaotic index
to seek the chaotic fluctuant law by studying comparatively American developed
stock market and Chinese developing stock market with Standard & Poor 500
Index, and Dow Jones Industrial Average Index. The chaotic degrees of Chinese
and American Stock Markets are compared firstly. Secondly, the features of
American Stock Market during the 50 years’ development are involved. And finally
the differences between the chaotic statuses of these two markets are analyzed.

Ø
**Professor Dr. WANG Rusong**

Research Center for
Eco-Environmental Sciences

Chinese Academy of Sciences

**Understanding the
Human Eco-Complexity: **

**Social-Economic-Natural
Complex Ecosystem Method and its application in China**

Unlike biological
communities, human society is a kind of artificial ecosystem dominated by human
behaviour, sustained by natural life support system, and vitalized by
ecological process. It was named by Shijun Ma a Social-Economic-Natural Complex
Ecosystem (SENCE). Its natural subsystem consists of the Chinese traditional
five elements: metal (minerals), wood (living organism), water, fire (energy)
and soil (nutrients and land). Its economic subsystem includes the
components of production, consumption, reduction, transportation and
regulation. While its social subsystem includes technology, institution and
culture (Fig.1).

In dealing with this complexity, people used to see physical
"being" rather than ecological "becoming", and pay much
attention to engineering structure, economic process and social function while
neglecting its system context. It is just
this synergetic function that economy, society and physical environment can
interact one another as to sustain a harmonized human ecosystem. According to
Lao Dan, a famous ancient Chinese philosopher, this sustaining function is
“such a thing which seems to forth from nowhere, and yet it penetrates
everywhere”. It is formless, shapeless, vague, indefinite, imperceptible and
indescribable, always changing, and reverting to the state of nothingness”. To
measure this nothingness, the critical issue is how to image the complicated
interactions, how to simplify and integrate the diversified relationship, and
how to develop a practical instrument for promoting the sustainable development.
SENCE method checks its internal mechanism of competition, symbiosis and
self-reliance; its process, pattern and order; its structural wealth,
functional health and people’s faith; its efficiency, equity and vitality; the
balance among the four driving forces of energy, money, power and spirit and
the human interference of technology, institution and culture, from both
internal and external, upper and lower scaling, long and short terms,
centralized and decentralized.

Taking Tianjin, the
third largest city in China as an example, this paper is trying to integrate
human ecology, system science, and philosophical views of cities into an urban
eco-complex model. It is a combinatory model
consists of mechanism model, planning model, and regulation model. A Pan-Objective
Ecological Programming method is introduced, in which the urban eco-complexity
is modeled through identification of its key
factors, feedback and function, and simulation of its partial problems, process
and alternative policies.

Ø
**Professor Dr. WANG Shouyang**

Institute of Systems Science

Academy of Mathematics and Systems
Sciences

Chinese Academy of Sciences

Computational Complexity of Arbitrage in
Frictional Market

Abstract. We are interested in computation of
arbitrage condition in financial market with friction. We consider a model with
a finite number of financial assets and a finite number of possible states of
nature. We derive a negative result on computational complexity of arbitrage in
the case when securities are traded in integer numbers of shares and with a
maximum amount of shares that can be bought for a fixed price.

Key Words: Computational complexity, Arbitrage, Frictional market

**French Participants**

Ø
**Jean-Pierre AUBIN**

Centre de Recherche Viabilité, jeux, Contrôle

Université de Paris-Dauphine

**Regulation of the
Evolution of the Architecture of a Network **

**by Connectionist
Tensors Operating on Coalitions of Actors**

Abstract: Neural networks, genetic networks and
socio-economic networks describe collective phenomena through constraints
relating actions of several actors, coalitions of these actors and multilinear
connectionist operators acting on the set of actions of each coalition. We
provide a class of control systems governing the evolution of actions,
coalitions and multilinear connectionist
operators under which the architecture of the network remains viable.
The controls are the "viability multipliers" of the "resource
space" in which the constraints are defined. They are involved as
"tensor products" of the actions of the coalitions and the viability
multiplier, allowing to encapsulate in this dynamical and multilinear framework
the concept of Hebbian learning rule in neural networks in the form of
"multi-Hebbian" dynamics in the evolution of the connectionist operators.
They are also involved in the evolution of coalitions through the
"cost" of the constraints under the viability multiplier regarded as
a price.

Ø
**Pierre CARTIGNY**

Maître de conférences, faculté de Sciences Economiques,

Université de la Méditerranée.

Greqam Marseille.

Détaché Inra de Montpellier.

**"Selection of One Nash Equilibrium in L-Q
Differential Games"**

An interesting question in
game theory is how to select a particular Nash equilibrium when there exists
more than one. In differential game theory, there has been very little attempt
to study criterions for selection. In a recent paper, Engwerda (Jota 1999)
studies this problem in the context of the standard one-dimensional
linear-quadratic non-zero sum game. Even in this very simple game, the
restriction to stationary linear feedback startegies does not permit to select
a unique Nash equilibrium. Selection criteria like stability or maximal total
gain do not seem robust. In this paper
we are interested by the standard one-dimensional linear-quadratic game with
two players and we restrict the set of strategies to (time-varying) linear
feedback strategies. Indeed our purpose is to select a unique Nash equilibrium
in infinite horizon case and it is a natural way to consider the associated finite
horizon game without penality. We show
that in finite horizon this game admits a unique Nash equilibrium which can be
simply characterized by using a time inversion. In infinite horizon, the
problem becomes less simple. A well-known difficulty of the infinite horizon
arises in optimal control theory : the transversality condition in infinite
horizon is not a necessary condition for optimality. As a consequence, we cannot easy characterize the Nash
equilibrium in infinite horizon (for a convex game) by conditions that are
necessary and sufficient. But because we want to select one Nash equilibrium in
infinite horizon, we do not need to study the set of these equilibria. For the
simple game which we consider, we show that the finite horizon equilibrium
strategies converge (for all fixed data) to a steady-state. And this
steady-state is precisely the constant linear strategies of one equilibrium in
infinite horizon. This criterion of selection, the limit of the finite horizon
Nash equilibrium is both simple and meaningfull (when it applies), because the
infinite horizon game can be interpreted as the limit of finite horizon games.

**Key Words**:Linear-quadratic
games. Nonzero sum differential games. Nash equilibria. Infinite horizon.

Ø
**Robert DELORME** (sous réserve)

Professor -
Versailles University

Research
Director - CEPREMAP - Paris

**Theorising Complexity**

** **

Ø
**Alan KIRMAN**

Institut Universitaire de France,

EHESS,

Université d’Aix-Marseille lll

The models which have been used in the
literature attribute a great deal of rationality to the agents concerned and
permits very limited conclusions. Here two approaches are suggested which
consider agents as essentially reacting to their previous experience rather
than anticipating events. The first uses a reinforcement learning rule which
can be justified theoretically and which produces stronger conclusions. The
second uses Holland's "classifier
system" approach and makes very limited demands on the agents. This produces
the most striking results as to the type of phenomena that emerge. All the
results are compared with the data concerning the trading relationships on
the Marseille wholesale fish market.

Keywords :
trading groups, learning, rationality

Ø
**Jacques LESOURNE**

Ø **Jean-Pierre
NADAL**

Laboratoire
de Physique Statistique

de
l'Ecole Normale Supérieure (CNRS UMR8550)

**Statistical Physics Approach to the
Modelling of Social Networks**

Abstract:
One of the main success of Statistical Physics is to explain
"emergent" properties as collective phenomena resulting from the
interactions between a large number of similar units. Making use of tools
developped in the context of the modelling of disordered systems, physicists
have analysed such "macroscopic" properties of various systems, in
particular neural networks, and in the recent years social networks (including
financial and economic markets). I will
illustrate this with one or two examples, including the case of the modelling
of "social clustering"
(formation of coalitions or groups).

Ø
**Jean PETITOT**

Studies Director at EHESS

Manager of CREA - Ecole Polytechnique, Paris.

**Perception
as a complex system : **

**the
functional architecture of the visual cortex.**

**Abstract
: **Forms are organized structures emerging from the
physics of the underpinning substrates. But they are also perceptive and
cognitive constructs processed by the brain. Due to the results of cognitive
visual neurosciences we begin to understand how the brain computes the geometry
of visual morphologies. We will take the most simple example: the integration
of visual contours from their distributed parallel implementation in the
cortex. How globally coherent macro forms can emerge in our percepts even
though they are implemented in millions of neurons detecting only very local
micro features? This astonishing performance results from the fonctionnal
architecture of the cortical visual areas, and from binding phenomena ensuring
a global coherence property.

Ø
**Jean SALLANTIN**

Directeur de Recherche CNRS

LIRMM 161 rue Ada 34392 Montpellier cedex

**Rationality
and Learning in Scientific Discovery**

**Abstract:**
The scientists act rationally to build a scientific knowledge representation
when they establish a correspondence (Carnap, 1931) between an empirical and a
theoretical knowledge representation.
The research of a corroboration (Lakatos, 1994) between an empirical and
a theoretical knowledge gives the dynamic of a scientific knowledge building.
Practical uses of a theoretical knowledge are explanation and prediction of
empirical phenomena. So the classes of scientific predictions and explanations
providing from the theory are more constrained than the candidate explanations
and predictions expressed with the apparatus of an empirical domain. In another
terms, the capacity of creativity, of liberty and of adequacy to the reality,
which belongs to an empirical language, is greater than those of the
theoretical one. In opposite, the computational and human learnability of a
knowledge is only possible when there is an adequacy (Kuhn, 1982; 1983) between
empirical and theoretical knowledge. In other terms, theory is efficient
mainly to formulate and explain an
existing empirical and technological discovery (Whewell, 1936). We shall present advanced applications to
the domain of transactions in Law and their applications to e-commerce. We
shall present some preliminary results of a pluridisciplinary working-group
(Computer science, Mathematics, Law, Philosophy and Anthropology) on “crisis,
conflicts and transaction in Networks”.

Ø
**Alexandre STEYER**

Professeur à l'Université de Paris I - Sorbonne

(and Jean-Benoît Zimmermann

Directeur de Recherche CNRS - GREQAM- Marseille)

Self
Organised Criticality in Economic and
Social Networks

The
Case of Innovation Diffusion

**Abstract:** Diverse approaches of
innovation diffusion, in the presence of increasing returns, have been outlined
or explored in the recent literature. We propose, four ourselves, to take into
account the idea that agents, in the situation to adopt or not an innovation or
a new technological standard, are “situated” within a social network, that is
the support of influence effects. Our approach aim is here to explore the role
of learning processes into the propagation dynamics within a network structure.
In a recent model, formally represented by a neural network, we have introduced
a **relational learning** that
constitutes a way to set up an endogenous network evolution . We prove the
existence of a **self organised
criticality** phenomenon, where some agents acquire key-positions within the
network that bring them a strong structural capacity of influence over the
whole population of potential adopters. In this paper, we study the way how
network auto-organisation can lead, under given conditions, to a critical state
characterised by macroscopic effects generated from microscopic impulses at the
level of the individual agent. It is the peculiar structure of those critical networks that allow macroscopic “avalanches” to take place,
on which the diffusion process is likely to lean. We analyse the way learning
leads endogenously to such a critical state and how it strikes against the
finite size of the network.

Ø
**Richard TOPOL**

Directeur de Recherche CNRS

CREA - Ecole Polytechnique

Paris

**Bubbles Volatility of Stock Prices: Effect of Mimetic
Contagion**

**Abstract**: The aim of the paper is to present a theoretical explanation of the
effect of the mimetic contagion on the dynamics of the market price as a
financial asset. It explains the birth, the life and the explosion of a
'contagion' bubble as well as the 'contagion' volatility of the price. The
paper has two characteristics. First, about the agents' economic behaviour: to
describe such situations where market traders know they have an incomplete
information set. I propose a 'fads' model in which any investor sets his bid
and / or ask prices according to an additive learning process. On the one hand,
he adjusts his prices to his present value calculated from his incomplete
information set. This is *'limited'
rational behaviour*. On the other hand to capture some information held by
the other investors, he also adjusts his prices to average prices of his
nearest buyers and sellers. This is *mimetic
contagion*. Stock price movement is then socially transmitted. Second, about
the mathematical treatment: to model a random process there are two mathematical
models. The first, and most familiar, models a discrete (continuous) random
process as a discrete (continuous) sequence of random variables. In the second
approach, the random process is constructed from an abstract dynamic system
which consists of a probability space together with a transformation on the
space which tell us how each configuration evolves with the time. The
statistical treatment used in this paper employs the former approach. To get
more general results with respect to the ergodic property, it may be worth
reformulating the problem within the framework of the latter, more abstract,
concept of dynamic system. The paper presents an unusual stochastic treatment
based on the equation of motion of the probability density function of the set
of bid and ask prices. A generalised Fokker-Plank equation, valid only on a
relevant time scale, is obtained. Then, the market price is defined as a
function of the bid and ask prices of the buyer and the seller who meet each
other to realise a contract. The mean and variance equations of the market
price are deducted from the generalised Fokker-Plank equation.

**General organization of the workshop**

** **

**Chinese part:**

** **

Ø
**Professor Dr.
HUANG Haijun**

School of Economics and Management

Beijing University of Aeronautics and Astronautics

Deputy Director of the Department of
Management Sciences,

National Natural Science Foundation
of China

** **

**French part:**

Ø Research Director at CNRS GREQAM-EHESS 2
Rue de la Charité 13002
Marseille Tel: (33) 04 91 14 07 37 Fax:
(33) 04 91 90 02 27 |
assisted by logistics: |
Ø Research Director at CREA Ecole
Polytechnique Paris Ø
Institut
Jean Nicot Paris |