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This book continues in a tradition which has developed in the annual Workshops on Economics with Heterogeneous Interacting Agents, (WEHIA). The purpose of that workshop was to analyse situations in which individual agents, who might be different from each other, interact and produce behaviour on the aggregate level which does not correspond to that of the average actor. This rupture with the well-established tradition of the “representative individual” is far from having established a central position in economics. That the relaxation of that assumption and the introduction of heterogeneous individuals might change the relationship between micro behaviour and macro phenomena is clearly spelled out by Forni and Lippi(1997). The modelling of the actual interaction between these individuals has been and remains a challenge. Early analytical attempts to introduce direct and local interaction between agents such as in the pioneering work of Follmer (1974) met with little response and the recent wave of interest associated with the names of Aoki (1996) Durlauf (1997) and Blume (1993) amongst others was twenty years in the making. Yet, the influence of other disciplines such as physics and biology in which complex interactive systems and their analysis play a central role is now making itself felt in economics and the papers in this volume reflect that fact.
Alan Kirman, Jean-Benoît Zimmermann

Social Networks


A Simple Model of Fads and Cascading Failures on Sparse Switching Networks

The origin of large but rare cascades that are triggered by small initial shocks is a problem that manifests itself in social and natural phenomena as diverse as cultural fads and business innovations (1–5), social movements and revolutions (6–8), and even cascading failures in large infrastructure networks (9–11). Here we present a possible explanation of such cascades in terms of a network of interacting agents whose decisions are determined by the actions of their neighbors. We identify conditions under which the network is susceptible to very rare, but very large cascades and explain why such cascades may be difficult to anticipate in practice.
Duncan J. Watts

Self Organised Criticality in Economic and Social Networks

The Case of Innovation Diffusion
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.
Alexandre Steyer, Jean-Benoît Zimmermann

Social Percolators and Self Organized Criticality

We discuss the influence of information contagion on the dynamics of choices in social networks of heterogeneous buyers. In the case of non-adaptive agents, the dynamics results in either the contagion process being stuck and very few agents actually buying (flops) or in a ‘hit’ where most agents a priori interested in getting the product actually buy it. We also show that when buyers and sellers try to adjust bids and asks the tatonement process does not converge to equilibrium at some intermediate market share and that large amplitude swings are actually observed across the percolation threshold.
Gérard Weisbuch, Sorin Solomon, Dietrich Stauffer

Lock-out in Social Networks

We introduce negative relationships in a network of social influence whose agents cope with a binary opinion concerning two competing standards, and we explore the possible collective dynamics. A weak proportion of anticonformism leads to well known phenomenon of lock-in (collective agreement uppon one given opinion). Too much anticonformism generates persistent instability in individual opinions about technological standards. Now, we point out that an optimal dose of anticonformism can originate lock-outs: a minimal amount is necessary to depart from homogenous behaviors, but too much would prevent the rest of the society from reaching the opinions of anticonformists, and achieve the lock-out. Hence, our interaction-ist analysis points out specific conditions of demand as a possible reason for changing consumer behaviors in a context of standardization.
Frédéric Deroian

Cooperation, Adaptation and the Emergence of Leadership

A generic property of biological, social and economical networks is their ability to evolve in time, creating and suppressing interactions. We approach this issue within the framework of an adaptive network of agents playing a Prisoner’s Dilemma game, where each agent plays with its local neighbors, collects an aggregate payoff and imitates the strategy of its best neighbor. We allow the agents to adapt their local neighborhood according to their satisfaction level and the strategy played. We show that a steady state is reached, where the strategy and network configurations remain stationary. While the fraction of cooperative agents is high in these states, their average payoff is lower than the one attained by the defectors. The system self-organizes in such a way that the structure of links in the network is quite inhomogeneous, revealing the occurrence of cooperator “leaders” with a very high connectivity, which guarantee that global cooperation can be sustained in the whole network. Perturbing the leaders produces drastic changes of the network, leading toglobal dynamical cascades.These cascades induce a transient oscillation in the population of agents between the nearly all-defectors state and the all-cooperators outcome, before setting again in a state of high global cooperation.
Martín G. Zimmermann, Víctor M. Eguíluz, Maxi San Miguel

From micro to macro behaviours


Technology Diffusion, Stability and Decay: some Results

The proposition that history matters is not new in the economic debate, but growing recognition that technological change matters for economic growth has renewed and rephrased that proposition in more formal if narrower terms. Rosenberg, Paul David and Brian Arthur are names associated with path-dependence. Ebeling et alit used Markov processes as a random walk, and de Araújo used a birth-and-death model as a stochastic equivalent of a diffusion equation for finite markets. The present paper further explores this line, with new results. By examining similarities and differences between the author’s results and those of others, we try to discern the implications of these assumptions for the results obtained on technology diffusion, and raise a few questions on the significance of stable equilibrium for analytic purposes. Finally, we discuss extensions to incorporate insights from other work aiming to arrive at a better understanding of the real processes of technology innovation and diffusion.
J. Lizardo, R. H. De Araújo

On Dynamic Re-Specifications of Kiyotaki-Wright Model

This paper examines the well-known Kiyotaki-Wright model for its dynamic specification. Because the authors are silent on the exact dynamic structure of their model, and on their model’s behavior off the equilibrium states, the model dynamics can be introduced in several ways. One such interpretation focuses on the fact that the number of money traders on and off equilibria is fixed exogenously. One of our modifications introduces a possibility for the number of money traders also to evolve with time.
Masanao Aoki

Industrial Dynamics with Quasi-Zero Intelligence Interacting Firms

This paper presents some artificial stylised facts emerging in a simulated contestable market where firms interact with each other in taking their stay or go decision. We use nearly zero-intelligence firms: no optimisation is considered, and all the firms sell at a fixed price an equal quantity of the good. The entry of new firms is triggered by the overall profitability of the market, measured with the spread between the average rate of profit and the interest rate. The exit decision is modelled via a mean field effect, to take into account in the decision process both the performance of the individual firm, and the information about the profitability of the market that can be abduced looking at the stay or go decision of the other firms. Financial requirements of production are considered, with a spread between creditor and debtor interest rates. The model is simulated with the ACE approach, using the Swarm libraries released by the Santa Fe Institute.
Roberto Leombruni, Domenico Delli Gatti, Mauro Gallegati



Stability of Pareto-Zipf Law in Non-stationary Economies

Generalized Lotka-Volterra (GLV) models extending the (70 years old) logistic equation to stochastic systems consisting of a multitude of competing auto-catalytic components lead to power distribution laws of the (100 years old) Pareto-Zipf type. In PartIcular, when applied to economic systems, GLV leads to power laws in the relative individual wealth distribution and in the market returns. These power laws and their exponent a are invariant to arbitrary variations in the total wealth of the system and to other endogenous and exogenous factors. The measured value of the exponent α = 1.4 is related to built-in human social and biological constraints.
Sorin Solomon, Peter Richmond

Toy Models of Markets with Heterogeneous Interacting Agents

Simple models of financial markets with heterogeneous adaptive agents have been recently investigated using tools of statistical mechanics of disordered systems. We review and discuss the main results of this approach.
Matteo Marsili

Price Bubbles and the Long Run Profitability of a Trend Following Technical Trading Rule

The model allows individual traders to endogenously choose between fundamental information and a technical trading rule. Since the technical trading rule works as a crude signal extractor, its profitability relies on price movements reflecting changes in the intrinsic value of the security. Sustainable profits can be earned using the technical trading rule. The trading rule’s popularity grows with its recent trading success, but excessive popularity diminishes the trading rule’s ability to extract a reliable signal. Parameter settings that allow large fluctuations in the technical trading rule’s popularity lead to unsustainable periods of positive profits coupled with long-term losses.
David Goldbaum

Firms’ Financial Heterogeneity and Business Cycles

In this paper I try to generalise the Greenwald-Stiglitz’s framework with equity rationing introducing firms’ financial heterogeneity as suggested by the hierarchy of finance model. After distinguishing among firms’ alternative financing regimes it is possible to establish both a short run non-neutrality proposition according to which monetary policy may affect real output through changes of the expected future price level, and a long run non-neutrality proposition based on the Fisher effect. Moreover, changes in the degree of financial fragility of the system, ‘proxied’ by changes in the proportion of liquidity constrained firms, may determine shifts of the dynamic behaviour of the system.
Marco Gallegati



Stable Coalition Structures with Fixed Decision Scheme

This paper studies the stability of coalition structures when coalitions must choose an alternative in a one-dimensional space, using a fixed decision scheme. This decision scheme depends on the preferred alternative of all agents in the coalition. We assume that the number of agent is finite. Hence, when an agent, or a group of agent, leaves a coalition and enter in another coalition, this will affect the outcome of the decision scheme in the former and the new coalitions. We provide in this paper sufficient conditions for the existence of stable coalition structures, for two stability concepts, namely C-stability and Tiebout-stability. The model presented here can be understood as a local public good economy with horizontal differentiation.
Guillaume Haeringer

Coalition Formation with Heterogeneous Agents

The paper analyzes a game of coalition formation in which agents with limited computational abilities possess heterogeneous endowments and seek to coax lesce into groups to produce and divide an output. The basic game is modelled as a two stage game; in the first stage every agent sends other agents various messages consisting in the proposal of a coalition. In the second stage, knowing the coalitions, agents choose the actions to perform. We show that there exists at least a Strong Nash equilibrium characterized by the consecutive property, i.e. the richest agents form a coalition among themselves and so do the poorest agents. The numerical simulations show that agents play the SNE with high probability; moreover, the more unequal the initial distribution of resources, the lower the average utility in the economy. The transition paths highlight the fact that the rich agents are the first to coalesce, so that the inequality of individual utilities increases in the early periods and then decreases when poor agents also start coalescing. In contrast, average utility is generally increasing, so that there exists a non linear relationship between inequality and average utility.
Davide Fiaschi, Pier Mario Pacini

Location Games with Externalities

We propose a two step game of coalition or city formation. In a first step, each player chooses the location in which he wants to be. The payoff function, determined in the second step by a game between the different locations reflects two effects: a public effect such that payoffs decrease with the number of non-empty locations; a private effect such that payoffs to the inhabitants of a PartIcular location decrease with the size of the population at that location. We analyse the consequences for the set of stable profiles of an increase in the relative weight of the public effect in the payoff function. We show that the number of stable profiles increases with the public effect but that the newly added profiles are not always more concentrated.
Jacques Durieu, Philippe Solal, Sylvie Thoron

Interactions and Knowledge


“Simon says...” What? Rationality of Imitation in a Simonian Perspective

In uncertain situations, decision-makers must find ways to simplify, assume and guess. One possible rule to adopt is to imitate some other agent. In this contribution we address the issue of mimetic behaviour as a possible rule for choice and action in uncertain contexts. More precisely, this paper provides an analysis of the rationality of imitative behaviours by using Simonian bounded and heuristic rationality paradigms.
We firstly look back to the concept of procedural, or rather heuristic, rationality in Simon’s works in which rationality is faced as cognitive processes. This step will lead us to the conclusion that the simplifying hypothesis of the substantiality of rationality is only relevant when the choice situation is simple. So, another apparatus is needed in situations of great uncertainty and complexity, when the only possible choice is to learn.
Secondly we go deeply into the analysis of Mimetism. After having recalled some necessary conditions to make this choice possible, we show how imitation corresponds to three conceptually different statuses: information, action and means of co-ordination. Then, we present how Mimetism is the output of a deliberation following three logical moments: identification of options, appraisal and choice.
Crossing rationality and imitation analyses leads us, thirdly, to present three types of mimetic rationality, each of them defining one kind of Mimetism as a specific learning process:positive Mimetism Mimetism of doubt and Mimetism of uncertainty.This taxonomy results from two main dimensions of analysis: the place of uncertainty in the process of choice, and the influence of cognitive entities on the agent’s decision.
Claire Charbit, Valérie Fernandez

Interacting Individuals and Organizations: a Case Study on Cooperations Between Firms and Research Laboratories

The issue of which kind of entities are really interacting is specifically central and difficult in the study of cooperations between research laboratories and firms, because these partnerships involve various kinds of agents.
Michel Grossetti, Marie-Pierre Bès

Organisational Innovation, Communities of Practice and Epistemic Communities: the Case of Linux

A growing number of works in the literature consider the process of production and circulation of knowledge within the firm as is the key determinant of the capability of the organisation to innovate Nonaka and Takeuchi, 1995; Leonard-Barton, 1995; von Krogh, Roos and Kleine, 1998, etc…). It is widely agreed that the “cognitive architecture” of knowledge within the firm (the way knowledge is produced, stored, exchanged, transmitted, retrieved) strongly influences the process of organisational learning, and in turn the innovative process. As Nonaka and Takeuchi (1995) emphasised, the process of creation of knowledge within firms relies on two main dimensions; the first one is the “epistemological dimension”: the critical assumption is that human knowledge is created and expanded through social interaction between tacit knowledge and explicit knowledge (“knowledge conversion”); the second one is the “ontological dimension” which is concerned with the levels of knowledge creating entities (individual, group, organisational and inter-organisational). In line with the assumptions initially made by Argyris and Schön (1978), the organisation supports creative individuals or provides contexts for them to create knowledge.“Organizational knowledge creation therefore should be understood as a process that organizationally amplifies the knowledge created by individuals and crystallizes it as a part of the knowledge network of the organization. This process takes place within an ”expanding community of interaction“ which crosses intra and inter-organizational levels and boundaries”Nonaka and Takeuchi, 1995. emphasised, the process of creation of knowledge within f1rms relies on two main dimensions; the first one is the “epistemological dimension”: the critical assumption is that human knowledge is created and expanded through social interaction between tacit knowledge and explicit knowledge (“knowledge conversion”); the second one is the “ontological dimension” which is concerned with the levels of knowledge creating entities (individual, group, organisational and inter-organisational). In line with the assumptions initially made by Argyris and Schön (1978), the organisation supports creative individuals or provides contexts for them to create knowledge.“Organizational knowledge creation, therefore, should be understood as a process that organizationally amplifies the knowledge created by individuals and crystallizes it as a part ofthe knowledge network of the organization. This process takes place within an ”expanding community of
Patrick Cohendet, Frederic Creplet, Olivier Dupouët

Knowledge Creation, Knowledge Diffusion and Network Structure

This paper models knowledge creation and diffusion as processes involving many agents located on a network. Knowledge diffusion takes place when an agent broadcasts his knowledge to the agents to whom he is directly connected. Knowledge creation arises when agents receive new knowledge which is combined with their existing knowledge stocks. Thus both creation and diffusion are network-dependent activities. This paper examines the relationship between network architecture and aggregate knowledge levels. We find that knowledge growth is fastest in a “small world”, that is, when the underlying network structure is relatively cliquish (dense at a local level) yet has short paths. This corresponds to a locally-connected graph which includes a few long-distance connections or shortcuts.
Robin Cowan, Nicolas Jonard


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