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In traditional economics models of perfect competition agent's interactions are all mediated through the market. Interactions are anonymous, global and indirect. This is a powerful model, but we see many instances in which one, and sometimes all, of the previous characteristics fail to hold true. The type of agent you are, or your identity, can affect the type of interaction we have, and most surely the relationship between micro-behaviour and macro-phenomena in non-trivial ways. This book contains a selection of papers presented at the 6th Workshop on Economics with Heterogenous Interacting Agents (WEHIA). The contributions show that work done in other fields like evolutionary biology, statistical mechanics, social network theory and others help us to understand the way in which economic systems operate. Virtually all of the papers presented in this volume draw on some aspect or other of these varied approaches to related problems.



Learning, Adaptation and Complex Dynamics


Heterogeneous, Boundedly Rational Agents in the Cournot Duopoly

A Cournot duopoly market modeled as a co-evolving system of autonomous interacting agents is investigated. We present results for different types of boundedly rational agents. Agent types differ both in the complexity of their strategies and the information they have available to make their decision. Some types of agents use very simple strategies to make a production decision, while other types use a quite sophisticated decision rule. All agents types are tested in a round robin tournament. We consider the evolutionary stability of the evolving populations, especially with respect to the different equilibria of the Cournot game. Furthermore, we investigate the performance of the different agent types under changing market conditions.
F. Alkemade, J. A. La Poutré

Adaptive Coordination and Aggregate Efficiency in Minority Games

This work studies the properties of a coordination game in which agents repeatedly compete to be in the population minority. The game reflects some essential features of those economic situations in which positive rewards are assigned to individuals who behave in opposition to the modal behavior in a population. Here we model a group of heterogeneous agents who adaptively learn and we investigate the transient and long-run aggregate properties of the system in terms of both allocative and informational efficiency. Our results show that, first, the system long-run properties strongly depend on the behavioral learning rules adopted, and, second, adding noise at the individual decision level and hence increasing heterogeneity in the population substantially improve aggregate welfare, although at the expense of a longer adjustment phase. In fact, the system achieves in that way a higher level than that attainable by perfectly rational and completely informed agents.
G. Bottazzi, G. Devetag, G. Dosi

Heterogeneous Models with Learning and Homoclinic Bifurcations

We analyze a class of models representing heterogeneous agents with adaptively rational rules. The models reduce to non invertible maps of R2. In particular we shall investigate the homoclinic bifurcation of the saddle fixed point, which causes the sudden transition to a chaotic attractor (or strange attractor, with self-similar structure).
I. Foroni, L. Gardini

Learning to Compete and Coordinate in a Complex World

We discuss a generic model of complex adaptive systems in which many heterogeneous agents compete to exploit a large number of resources. The agent-agent interaction mixes coordination and competition. We discuss how the collective behavior can be quantified and the main results which have been recently derived by the statistical mechanics approach. Then we study how a population of heterogeneous agents with finite memory learns to coordinate in a such a complex world. We show the existence of equilibrium and dynamic phase transitions as a function of the memory and the learning rates of the agents. A too short memory prevents agents from reaching optimal coordination. Furthermore, in a non-stationary environment, we show by numerical simulations that the phase transition becomes discontinuous. These effects arise as a consequence of a feedback loop of endogenous fluctuations on the learning dynamics of agents.
M. Marsili, R. Mulet, F. Ricci-Tersenghi

A Model of Distributed Markets with Heterogeneous Agents

We consider a model of heterogeneous, inductive rational agents, who interact through an aggregate, collective variable, and act on a finite system of local markets, where they play the Minority Game (MG). The markets have their local histories. Any agent at any time can play only on a single local market, but over time they may change the market according to certain rules. In this paper we focused on the differences and similarities between MG played on one single market (global market) and MG played on a system of local markets.
T. Płatkowski, M. Ramsza

Micro Foundations of Macro Behaviour


An Exact Physical Approach to Market Participation Models

Some new approaches to macroeconomic modeling describe macroscopic variables in terms of the behavior of a large collection of microeconomic entities; we give an exact model able to unify a large number of hypotheses introduced in this approach. Our treatise starts from the best known discrete model of classical Statistical Physics, the Ehrenfest urn model. The main generalization we perform consists in introducing “choice correlations” between agents, that give rise to “herd behavior” if they are strong and positive. These processes are homogeneous Markov chains whose transition matrix is determined by a parameter vector describing probabilities and correlation in state changes. The model is exactly soluble for most interesting cases. From applications to the clustering of agents the Ewens Sampling Formula is derived in an exact simple way, as a limiting case of our chain. Applications to stock price dynamics are shown. High positive correlation between market participants explicates the large observed values of kurtosis of the price increments.
U. Garibaldi, M. A. Penco, P. Viarengo

Financial Fragility, Heterogeneous Agents’ Interaction, and Aggregate Dynamics

According to the traditional view of the business cycle, large fluctuations are due to some impulses propagated throughout the entire economy (the so-called impulse-propagation approach). One of the puzzles it has to face is why large fluctuations arise without large shocks, since empirical evidence shows that there is not such a causal connection (Balke and Fomby 1994).
G. Giulioni, D. Delli Gatti, M. Gallegati

Heterogeneous Interacting Economic Agents and Stochastic Games

Stochastic games offer a rich mathematical structure that makes it possible to analyze situations with heterogeneous and interacting economic agents. Depending on the actions of the economic agents, the economic environment changes from one period to another. We focus on stationary equilibrium, the simplest form of behavior that is consistent with rationality. Since the number of stationary equilibria abound, we present the stochastic tracing procedure, a method to select equilibria. Since stationary equilibria are difficult to characterize analytically, we also present a numerical algorithm by which they can be computed. The algorithm is constructed in such a way that the equilibrium selected by the stochastic tracing procedure is computed. We illustrate the usefulness of this approach by showing how it leads to new insights in the theory of dynamic oligopoly.
P. J.-J. Herings, R. J. A. P. Peeters

Modeling Behavioral Heterogeneity in Demand Theory

This paper is a first step in answering B. de Villemeur’s (1998, 1999) and Hildenbrand’s (1998) criticism of the notions of behavioral heterogeneity introduced in demand theory by Grandmont (1992) and Kneip (1999). As in the Grandmont-Kneip approach, we define a notion of behavioral heterogeneity such that if the population is sufficiently heterogeneous, the aggregate budget share function is proved to become insensitive to changes in prices and income. However, in contrast to the aforementioned literature, this insensitivity in the aggregate is not explained by any insensitivity property at the microeconomic level, but rather by a “balancing effect” : For any commodity, the negative effect on market budget share induced after a change in prices or income by individuals who decrease their budget share is compensated by the existence of individuals who increase their budget share.
I. Maret

Social Interactions and Networks


The Joint Dynamics of Networks and Knowledge

In this paper the evolution of networks is studied in an environment where innovation takes place as a result of agents bringing together their knowledge endowments. Agents freely form pairs that must constitute a stable matching in which the rankings are made on the basis of the innovative ability of any possible pair. Once innovation has taken place the new knowledge generated is allocated to the individuals as a function of their joint profile and the process is iterated. We study the properties of the dynamic network formed by these interactions, and the resultant knowledge dynamics. We find evidence that the substitution patterns between different types of knowledge and the details of the way partners pool their knowledge is of great importance in determining first the emergence of expertise of a certain type in the economy, and second the stability of a number of network structures.
R. Cowan, N. Jonard, J.-B. Zimmermann

Stable Hedonic Networks

We consider a model in which players can form links between themselves under mutual agreement, and the set of all pairwise agreements is called a network. We stress that we are particularly interested in the case when some players are antagonistic, i.e., that they are separately “desirable” for someone, but “undesirable” when they are together. We define a class of preferences that ensures the stability of networks, if each player is sensitive to her direct neighbors only. However, it turns out that if players are sensitive to their indirect neighbors, antagonism between player may easily prevent stable networks to exist, for a large class of preference profile.
G. Haeringer

A Dynamic Model of Job Networking and Persistent Inequality

Although it rarely appears in economic models, job networking is a common feature of labour market behaviour. This paper develops a model of the macroeconomic implications of job networking for the behaviour of employment rates in an economy or community. I find that the spillovers created by networking produce a highly nonlinear relationship between community human capital and community employment rates. The model can be applied to understand the emergence of a low-employment “underclass” community in which even highly skilled or motivated individuals face severe employment difficulties.
B. V. Krauth

Bandwagon Effects on Female Labour Force Participation: An Application to the Netherlands

A major development in the second half of last century was the strong increase in married women’s labour force participation in many OECD countries. In particular, in the Netherlands the time pattern was quite pronounced. To explain this pattern this paper develops a dynamic model of bandwagon effects in female labour force participation. The model is formulated in terms of social-group variables, but it is derived in a systematic (be it approximative) way from an underlying individual labour supply model. The non-linear bandwagon dynamics are shown to imply long-run elasticities of the participation rate with respect to wage rate and other exogenous variables which vary with the level of the participation rate according to a hump-shaped profile. This leads to a sigmoid shape of the time profile of the participation rate which is considerably “sharper” than the logistic shape implied by static labour supply models. Such a time profile accounts in a stylized way for the Dutch pattern.
M. C. M. Vendrik

Interacting Agents and Continuous Opinions Dynamics

We present a model of opinion dynamics in which agents adjust continuous opinions as a result of random binary encounters whenever their difference in opinion is below a given threshold. High thresholds yield convergence of opinions towards an average opinion, whereas low thresholds result in several opinion clusters. The model is further generalised to threshold heterogeneity, adaptive thresholds and binary strings of opinions.
G. Weisbuch, G. Deffuant, F. Amblard, J.-P. Nadal



An Interacting-Agent Model of Financial Crises

This paper proposes a model of international financial crises that is based on the statistical mechanics. In our model the international stock market is composed of tow groups of traders mutually influencing each other with respect to their decision behavior, and financial contagion between markets occurs as a result of attempts by traders in the domestic market to imitate the behavior of traders who participate into exchange in a foreign market. This provides a channel through which a crisis in one market such as contemporaneous stock market crashes can transmitted to other markets. We show that the model can explain the stylized facts characterizing periods of recent international financial crises.
T. Kaizoji

Mean Field Effects and Interaction Cycles in Financial Markets

In this work, we investigated the effects of herding on assets price dynamics during the intra-day trading. The model — built as a mean-field in a binary setting (buy/sell decisions) — shows that when the interaction among individuals is low — i.e. there is few herding — the dynamics converges monotonically or with oscillations to the prior about the fundamental value of the asset (assumed constant and homogeneous across individuals). If agents give a larger weight to the action of the others fluctuations are amplified, until a Hopf bifurcation eventually occurs and limit cycles emerge. Simulations with gaussian noise on prices reproduce the same dynamics: rising either the strength of interaction or the intensity of choice the imitative behavior prevails on all other factors, and we have upward and downward rushes. For a wide range of “intermediate” values of parameters, some other interesting features emerge, such as excess kurtosis and clustering in the volatility of returns.
R. Leombruni, A. Palestrini, M. Gallegati

The Genoa Artificial Stock Market: Microstructure and Simulations

This paper presents an artificial financial market based on heterogeneous agents which are endowed with a limited amount of cash and one traded asset. Agents make random buy and sell decisions which are constrained by their limited resources and depend on the past price volatility. The price formation process is given by the intersection of the supply and demand curves.
M. Marchesi, S. Cincotti, S. M. Focardi, M. Raberto

Growth and Dynamics


A Simple Quantity Adjustment Model of Economic Fluctuations and Growth

This paper analyzes a new model of economy with several sectors which face quantity constraints, and show that business cycles and growth are present in this simple model. The sizes of sectors either increase or decrease stochastically, depending on the signs of the sectoral excess demands. We assume that allocation of resources is not instantanesous, and rely on the notion of holding time of continoustime, discrete-state Markov processes to select the sector that changes its size. Not only the output of this model fluctuates, but also, and more importantly, the level of the aggregate economic activity depends on the pattern of demands of the sectors of the economy. The greater is demands for high productivity sectors, the higher is the expected values of the model outputs.
M. Aoki, H. Yoshikawa

The Phillips Curve as an Attractor in a Dynamic Macroeconomic Model

In this paper the Phillips curve is derived as the image of a chaotic attractor of the state variables of a non-linear dynamical system describing the evolution of an economy. This has two important consequences: the Phillips curve in the model is a true long-run phenomenon and it cannot be used for policy purposes. The model is based on an overlapping-generations non-tatonnement approach involving temporary equilibria with stochastic rationing in each period and price adjustment between successive periods. In this way it is possible to obtain complex sequences of consistent allocations allowing for recurrent unemployment and inflation.
L. Colombo, G. Weinrich

Technical Progress in a Dynamic Input-Output Model with Heterogenous Labour

This paper introduces a dynamic input-output model with different skillgroups of workers. Exogenous technical progress is introduced as sector and skill-specific labour input coefficients are gradually falling over time. We discuss the effects of this kind of technological progress on the changing structure of the economy and the labour market performance of skilled and unskilled workers. As prices do not adjust immediately to unit costs, temporary rents emerge which are invested and thus enables the economy to grow at a faster than the equilibrium growth rate. Further, the sector and skill-specific technical progress implies changes in relative prices over time which then cause consumption demand changes due to substitution effects in the demand structure.
R. Stehrer


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