Workshop CNRS-NSFC on

Complexity in Social and Cognitive Sciences

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

Abstract:  Economic complexity is critical in understanding two fundamental issues in economic science: the origin of division of labor and the nature of persistent business cycles, which could not be explained by equilibrium economics.

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

Chaos in Business Administration

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


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

ABSTRACT         China is experiencing rapid growth in urbanization and industrial transition.  The pace, depth, and magnitude of these changes, accompanied by the persistence of past practices threatening to the regional and global environment and human well-being.  Sustainability can only be assured with a human ecological understanding of the complex interactions among environmental, economic, political, and social/cultural factors and with careful planning and management grounded in ecological principles. 

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,


Université d’Aix-Marseille lll

Learning To Trade

Abstract: Markets are an obvious example of complex adaptive economic systems. They have a certain number of features which are difficult to explain with models based on isolated anonymous maximising individuals.  For example, it is known that in many markets, individuals typically trade with very few partners. Thus markets are characterised by small trading groups. How the choice of trading partners  is made is one of the fundamental problems in economics. Typically, in most economic models, either those with whom one trades are given exogenously or one assumes some anonymous mechanism through which trade takes place. The purpose of this paper is to examine the conclusions drawn from different learning models in a simple market framework where individuals can choose their trading partners. They make their choices in function of their previous experience with different partners. I examine how the market organises itself into a trading network and analyse the characteristics of such networks.


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.




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


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      Jean-Benoît Zimmermann   

Research Director at CNRS          


2 Rue de la Charité             

13002 Marseille                              

Tel:  (33) 04 91 14 07 37               

Fax: (33) 04 91 90 02 27


assisted by






Ø      Paul Bourgine

Research Director at


Ecole Polytechnique Paris


Ø      Laure Cartron

Institut Jean Nicot