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Simulations in Economics: Methodological and Historical Perspectives

The Many Faces of Agent-Based Computational Economics: Ecology of Agents, Bottom-Up Approaches and Paradigm Shift

Les modèles multi-agents en économie, entre agents hétérogènes, approches bottom-up et changement de paradigme
Sylvain Mignot et Annick Vignes
p. 189-229


Cet article montre comment les modèles à base d’agents en économie computationnelle contribuent à l’étude des systèmes économiques. Leur apport à notre compréhension des mécanismes d’interactions sociales et de coordination est souligné, et les dépendances complexes entre niveau micro et niveau macro sont mises en évidence. Une première partie souligne les différences et les complémentarités entre l’approche computationnelle basée agents et les autres méthodes quantitatives. Une deuxième partie explique comment l’éconophysique peut fournir un cadre théorique alternatif pour une nouvelle science économique. Une troisième partie montre comment ces outils d’analyse permettent une meilleure représentation du fonctionnement de certains marchés comme les marchés financiers, les marchés du logement ou les marchés de biens halieutiques. En modélisant des agents hétérogènes et les règles qui déterminent leurs interactions, l’approche basée agents montre à quel point le fonctionnement des marchés dépend à la fois de leur architecture, du type de biens échangés et de l’écologie des agents.

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1. The Use of Agent Based Computations in Economics in Historical Perspective

1It can be argued that an economic system consists of heterogeneous agents acting on and responding to the aggregate states they all contribute to create (Napoletano, 2018). These agents regularly adapt to a perpetually changing world, in which human cognition, interactions and specific behavioral rules play a key role. These hallmarks of complexity call for tools which allow to model different nonlinear dynamics. Both micro and macro trajectories need to be calculated. This requires the development of new theories as well as new methods of modeling and empirical analysis.

2This paper presents an overview of how agent-based computational economics (ACE) contributes to the study of markets at both the macro and micro levels. ACE is a field of computational economics which aims to represent real world economic systems through the computational modeling of economic processes as open-ended dynamic systems of interacting agents. The dynamics of these systems are driven by the successive interactions of their participant entities. Agent-based models (ABMs) are the tool traditionally employed by ACE researchers to study economies as complex evolving systems, i.e., systems composed of many interacting units evolving over time.

3The paper starts by highlighting the interlinks and complementarities between agent-based models and other approaches for modeling social interactions and social mechanisms, such as experimental economics, econometrics or econophysics. It then explains how agent-based modeling (ABM) and the other alternative methods can increase our understanding of the functioning of markets when the quality of the exchanged goods is uncertain or when agents differ in their preferences or risk aversion. Modeling the specific aspects of heterogeneous agents and the rules driving their interactions brings to light the fact that the functioning of a market strongly depends on its architecture, the characteristics of the good exchanged and the ecology of the agents.

4ABM is part of the vast movement of computerization of economics that started in the 1930s (Backhouse and Cherrier, 2017). Microsimulation was invented by Orcutt (1957): this technique uses a set of data describing a population and applies rules to reflect changes, enabling the modeler to look at the overall impact. However, although allowing for heterogeneity, microsimulation does not model the interactions between the different elements. Only with the arrival of ABM did the modelling of interactions between agents become possible (Gilbert and Troitzsch, 2005; Fontana, 2006). ABM then descends from Von Neumann’s theory of automata and its developments (Von Neumann and Burks, 1970; Holland and Burks, 1970) which offer wider behavioral modelling capabilities.

  • 1 See Gallegati and Kirman (2012) and Ballot, Mandel, and Vignes (2015) for detailed presentations of (...)

5With the increase in computing capacities, ABM has continued to develop through ever more sophisticated models.1 In the context of social sciences, the “agents” in ABM models can represent individuals, social groups (firms, institutions, etc.), biological entities and/or physical systems (transport systems, etc.), which interact through prescribed rules (Farmer and Foley, 2009). The agents can be as diverse as needed, from consumers to policy makers or diverse institutions such as banks, firms or governments. At any given time, each agent acts according to its current situation, the state of the world and the rules governing its behavior. The algorithms allow to keep track of the many interactions, to see what happens over time. While agents of a socio-economic system differ in their preferences, constraints, objectives and organization, their interactions influence the outcome of the system and can be analyzed through an agent-based model. Agent-based modeling offers powerful new forms of hybrid theoretical-computational work which are particularly relevant to the study of non-equilibrium systems, i.e., systems in which macroscopic equilibrium is not attained despite orthodox utility maximization at the individual level (Epstein, 1999).

6These models are currently used to explain different economic phenomena and to give micro foundations to macro topics. They provide useful policy tools (Ghorbani et al., 2014) for policy makers to simulate an artificial economy under different policy scenarios and quantitatively explore their consequences. For example, the consequences of monetary policies can be simulated, when the economic environment varies and exogenous shocks occur. There are too many examples to list them all. Salle et al. (2013) investigate the performances of an inflation-targeting regime in a learning economy framed as an agent-based model. Keeping their framework as close as possible to the original New Keynesian model, they model the individual behavior of the agents under procedural rationality à la Simon. ABM is widely used to determine the most appropriate combination of fiscal and monetary policies in economies subject to banking crises and deep recessions. Dosi et al. (2015) study this issue using an agent-based model that is able to reproduce a wide array of macro- and micro-empirical regularities. Recent studies investigate the effects on the economy of a feed-in tariff policy mechanism aiming to foster investments in renewable energy production capacity (Ponta et al., 2018).

  • 2 A bottom-up approach to complexity consists in deducing the macroscopic objects and their complex p (...)

7Economic crises highlight the limits of mainstream economics in its analysis of the functioning of markets. They emphasize the urgent need for methodologies suitable for a better representation of path dependencies. Real markets are characterized by heterogeneity: heterogeneity of agents, goods, organizations, space and scale.2 The interactions between agents (individuals and/or organizations) greatly influence the outcomes of what we can now study as complex systems (Gallegati and Kirman, 2012).

8To tackle these different problems, other approaches than ABM have been developed, often interlinked. Experimental economics offers methods to measure individual preferences and the heterogeneity of human behavior. Econophysics uses methods from statistical physics to study stochastic processes and nonlinear dynamics. Econometrics uses statistics to describe the behavior of economic systems. We believe that existing and possible synergies between these approaches have great potential for improving our understanding of complex socio-economic systems.

9ABM has been extensively used to study the functioning of different markets. The higher the diversity of the products, the higher the uncertainty: on risky markets with weak or no quality signals, agents develop different strategies, according to their information or their level of risk aversion. Among others, we can quote the use of agent-based models to analyze “network markets” such as those for electricity (Gallo, 2016) or to understand the functioning of “new markets” such as carbon emissions trading (Tang, 2017; Hoekstra, 2017).

10A first contribution of this article (Section 2) is to clearly describe how ACE and other quantitative methods found in econometrics and experimental economics differ and complement each other. A second contribution (Section 3) is to explain the input of statistical physics to economics in the domain of ABM and to bring to light the convergence between these different fields of science. (Section 4) underlines the role of these alternative tools in the understanding of specific markets such as financial, housing or fish markets. At first glance, these markets seem very different. However, they all have highly volatile price distributions. Social phenomena like loyalty, herding behavior or social attractiveness largely influence the market outcome. Understanding the formation of prices and explaining the emergence of prices dispersion for similar goods require other methodological tools than the neo-classical equilibrium paradigm. In this section, we underline the contribution of alternative tools as econophysics, experimental economics or ACE. ABM helps to measure the influence of loyalty on fish markets (Mignot and Vignes, 2016); it allows to explain the emergence of social segregation on housing markets (Gauvin et al., 2013; Pangallo et al, 2019) or financial market bubbles (Fagiolo et al., 2019). This discussion brings fresh insights to a broader and very long-standing debate about the conditions of efficiency of market structures. A conclusory section discusses the specifics of ABM in the understanding of certain social phenomena.

2. ACE and Other Methods in Economics

  • 3 We thank one anonymous referee for providing us with this clear definition of how ABM is used.

11ABMs are used for integrative understanding: to figure out the aggregate pattern when we only know how individual elements behave. They are also used for differential understanding: we know the aggregate pattern and we want to find the behavior of the elements that could generate that pattern.3 Other methodologies exist which can contribute to the understanding of interactions and heterogeneous behavior, with their own advantages and disadvantages. Using them in conjunction with ABM can sometimes prove to be a fruitful approach. In what follows, we reflect on existing and potential synergies between ACE and its orthodox counterparts. We first interrogate (subsection 2.1) the synergy and convergence of ACE methods and the different econometrics methods. A second part presents the complementarity between ACE and experimental economics (subsection 2.2). The last part (subsection 2.3) shows how ABMs are used in agricultural economics, in the coupled human and natural systems approach. This approach is of special importance to study the dynamical two ways interactions between humans and their environment and to fight against climate change.

2.1 ACE and Econometrics: Synergies and Convergences

12Most of the techniques in econometrics aim to measure the behavior of an economic system, at either macro or micro level. When the way from one level to the other is not linear, because of the agents’ interactions and other loss of information, econometric techniques are inadequate for explaining the transition. In other words, faced with economic systems that exhibit complexity, uncertainty, volatility, or heterogeneity, econometric models provide weak understanding or predictions of the economic-behavioral processes. Economic systems are dynamic and seldom in equilibrium; no unique time-invariant econometric model is capable of capturing these aspects (Judge, 2016). Recently, a non-traditional econometric approach has been developed. This method recognizes that our knowledge of the underlying behavioral system and observed data process is partial and incomplete. It then suggests a self-organized, agent-based, algorithmic-representation system that involves networks, machine learning, and an information-theoretic basis for estimation, inference, model evaluation, and prediction.

13Because of heterogeneity, the aggregation issue is crucial. Part 2.1.1 below introduces a field little explored, although of major concern, which deals with the aggregation problem. Part 2.1.2 then explains how econometric techniques can be used to validate or estimate agent-based models and then reinforce their explicative properties.

2.1.1 ACE and the Aggregation Issue

14Rather than proposing even more complicated dynamic optimization schemes for representative agents, it makes sense to explore the patterns that may develop from aggregation over heterogeneous individuals, who make simpler but still coherent calculations (Kirman, 1992). To this end, ACE uses a bottom-up approach that does not need strong assumptions regarding individual behavior to obtain a tractable aggregation, allowing modelers to include more realistic behavioral rules in the aggregation, such as learning, coordination and interactions. ABMs generate data describing interacting, heterogeneous, boundedly-rational individuals. Once generated, econometric tests are estimated on this data, to check the robustness of results when faced with heterogeneity (Chen et al., 2009).

15As Stoker (1993) notes, one of the biggest challenges in tracking economic activity over time is assessing the impact of the changing composition of the economic players and/or their diversity. Two major approaches concern the empirical modeling of aggregate data: i) modeling aggregate data, based on the representative agent assumption, ii) modeling individual economic behavior through microsimulation. These approaches differ in terms of their treatment of the problem of aggregation over individuals. The first approach relies on the existence of a stable model among aggregates, and then fits the model statistically. Leaving aside the heterogeneity between agents, it carries out behavioral modeling at the micro level. The second approach to modeling aggregate data is microsimulation. This begins with a full model of the behavior of each type of individual in the population: aggregate values are then simulated by adding up across all individuals.

16Because ABMs are composed of many heterogeneous agents interacting with each other and with the environment, aggregation is not a simple matter and must be performed numerically, by counting and summing up individual quantities. Therefore, the aggregate properties of an agent-based model strongly depend on the complexity of the interactions among the different elements and the different micro or macro layers of the system. The micro level characteristics, i.e., learning rules, diversity, network structure and externalities produce macro level patterns. These macro level patterns can exhibit unexpected properties, which usually differ from the property of a system with one single representative individual. Aggregate phenomena exhibiting these unanticipated properties are commonly referred to as emergent.

17The need for a computational solution to the aggregate dynamics of agent-based models is equivalent to the need for a computational solution in the dynamic stochastic general equilibrium (DSGE) models. Nevertheless, in the DGSE classes of models, aggregate properties can be analytically understood or derived from first principles and primitive assumptions, contrary to ABMs where the aggregation of different individual behaviors does not generally inherit the properties of those behaviors.

2.1.2 Econometrics to Validate or Estimate ABM

18The use of econometrics to validate or estimate agent-based models started in the late 1990s (Miller, 1998). Agent-based models are arduous to estimate due to the lack of tractable criterion functions (likelihood functions, moments). But this problem is largely shared by many other econometric models and has been studied for a while. It has inspired the development of entirely new procedures based on simulation, known as simulation-based econometric methods.

  • 4 See Fagiolo et al. (2017) for a recent critical review of existing validation techniques.

19Given the flexibility of the ACE approach, there are many different ways to estimate the results—as well deciding which results to estimate—(Alfarano et al., 2005, 2006, 2007). The most commonly used estimation methods are the method of moments, maximum likelihood estimation and the least squares, either ordinary (Manzan and Westerhoff, 2007) or nonlinear (De Jong et al., 2009). An influential article by Windrum et al. (2007) examines a set of methodological problems arising in the empirical validation of agent-based economic models and discusses how these are currently being addressed. It has two objectives: to identify a set of issues common to all modelers engaged in empirical validation, and to discuss the three main alternative methodological approaches being developed in agent-based economics (indirect calibration, the Werker-Brenner approach, and the history-friendly approach). What follows underlines the similarities between econometric techniques and ABM when it comes to empirical validation. The methodological breakthroughs discussed here are numerous. They concern the lack of a core set of theoretical models applied to a wide range of research areas, the lack of comparability between models, the lack of standard techniques for constructing and analyzing agent-based models, and finally the issue of the empirical validation of the models.4

20Grazzini and Richiardi (2015) study the estimation of agent-based models. Their article proposes some directions for circumventing two difficulties that can arise when estimating ABM: i) the criterion function has no simple analytical expression and ii) the aggregate properties of the model cannot be analytically understood. They show under which conditions ergodic models can be consistently estimated by simulated minimum distance techniques, both in a long-run equilibrium and during an adjustment phase. The method they develop is defined as “simulated minimum distance”. This method has since been used by Bargigli et al. (2018) to show that meta-models can replicate empirical data. Grazzini et al. (2017) propose an alternative to this simulated minimum distance by using Bayesian inference techniques. In the last few years, many validation methods have been developed to measure the distance between real and simulated data. Simulated data are produced either by an agent-based model (Lamperti, 2015; Recchioni et al., 2015; Barde, 2017; Guerini and Moneta, 2017), or from a surrogate model (Salle and Yıldızoğlu, 2014; Lamperti et al., 2018b).

2.2 Experimental Economics and ACE

21When it comes to observing the diversity of individual behaviors, experimental economics (ExpE) has proved its worth. Nevertheless, possible synergies between ACE and ExpE are numerous, as they both aim to produce experimental evidence in controlled conditions. We will now describe the differences between ExpE and ACE and explain how they complement each other (Duffy, 2006; Contini et al, 2006). They have both benefited from the rise in computing power. The goal of experimental economics is to investigate individual behavior and the emergence of aggregate regularities through analysis of human subject experiments (Kagel and Roth, 1998; Kahneman and Smith, 2002). ACE focuses on the relationship between the micro and macro levels through artificial experiments. It searches for causal mechanisms grounded in the successive interactions of agents operating within computationally-rendered virtual worlds. Both methodologies use experiments to test or formulate theories, and both study how the macro level reflects individual behaviors. Both methodologies reject the assumption of a strictly rational homo-economicus, with unlimited cognitive and computing capabilities. While ACE tracks systems dynamics and path dependencies, both ACE and ExpE emphasize the role of heterogeneity, bounded rationality and learning.

  • 5 See Huang (2015) for a recent review.

22There is a branch of physics literature called “experimental econophysics”.5 It is based on controlled human experiments developed by physicists to study certain problems related to economics. These laboratory experiments are coupled with agent-based modeling (for computer simulations and/or analytical theory) in an attempt to reveal the general cause–effect relationship between specific conditions and emergent properties of real economic systems. The similarities between experimental econophysics and experimental economics coupled with ABM are so strong that it is hard to find a significant difference between the two approaches, and it feels like experimental econophysics is actually experimental economics coupled with ABM done by researchers with a background in physics.

23Duffy (2006) shows how ABM can help to explain results obtained from experiments on subjects. He points out two contributions of ACE to ExpE: i) the possibility of replacing some of the human subjects with artificial agents (and observing whether and how the behavior of the remaining humans changes) and ii) the use of ABM to simulate empirical facts found in laboratory experiments, in order to validate behavioral models. Contini, Leombruni, and Richiardi (2006) propose a classification of topics for which synergies between ExpE and ACE can be found. The following list summarizes this classification.

  • ACE toward experimental economics:

1. Design of human subject experiments.

2. Interactions between human and artificial agents.

3. Investigation of cognitive processes that lead to observed individual behavior in human subject experiments.

4. Benchmark comparisons of individual behaviors in human subject experiments.

5. Replication of human subject experiments with extended periods of interaction and number of agents.

  • Experimental economics toward ACE:

6. Benchmark comparisons of emergent features in agent-based simulations.

7. Use of experimental results for the specification of individual behavior.

8. Investigation of the unintended effects of the behaviors of human subject.

  • Using ACE to design experiments (topic 1): experiments with real human agents being costly, simulating the experiment to improve the design before implementing the real one sounds like an efficient method. Duffy (2001) drives an artificial agent-based computational approach to understand and design laboratory environments in which to test Kiyotaki and Wright’s search model of money. The behavioral rules of artificial agents are modeled on the basis of prior evidence from human subject experiments. Klingert and Meyer (2012) suggest an iterative, incremental procedural model as a framework for the collaboration between researchers in experimental economics and ABM modelers.

    • 6 In “experience-weighted attraction” (EWA) learning, strategies have attractions that reflect initia (...)

    Interactions between human and artificial agents (topic 2): at the crossroads of experimental economics and ACE, we can find experiments using humans and artificial agents simultaneously. Shachat and Swarthout (2012) design an experiment in which humans repeatedly play games against a computer program that follows either a reinforcement or an experience-weighted attraction learning algorithm.6 Grossklags and Schmidt (2003) study how software agents influence the market behavior of human traders and shows that common knowledge about the presence of software agents triggers more efficient market prices.

  • Benchmark comparisons of individuals and algorithms (topics 4 and 6): the idea of autonomous agents was motivated by the observation of human behavior (Chen, 2012) and it is only natural that comparative studies should emerge of human subjects on one side and autonomous agents on the other. It is indeed possible to create a copy of a human subject experiment and populate it with artificial agents, or (although this is more complex and costly) to mirror an ABM model using an experiment with human subjects. One of the pioneers was Jasmina Arifovic in the 90s, who replicated experimental results using artificial agents (Arifovic, 1994, 1995, 1996). Jager and Janssen (2002) demonstrate how decision rules based on psychological theory can be attributed to agents. These decision rules are then experimented with, in different settings. In these simulations, the agents can mimic the individual behavior of real people acting in a resource dilemma. Software agents are able to replicate the behavior of human subjects in the laboratory tests of markets, and have the potential to be used effectively in testing electricity auctions (Oh and Mount, 2011). More recently, Klingert and Meyer (2018) provide an example of how experimental data help to validate agents’ strategies on the micro level using statistical methods in the context of sales forecasting.

    • 7 The test of an algorithm’s ability to generate behavior that an external observer cannot distinguis (...)

    Specification of human behavior (topics 3 and 7): in a key paper, Arthur (1993) explores the idea of generating theoretical economic agents that behave like human agents and using them in neoclassical economic models. Two kinds of calibration mechanism are proposed. The first, statistical one fits parameters of the agents to empirical data. The second recommends using a Turing test.7 The first type of calibration is the one most commonly found in the literature. For example, in the article by Amin et al. (2018), a human-subject experiment was conducted to classify agent types and determine their effects on contribution levels. The data from the experiment was used to build and calibrate an agent-based simulation model. Similarly, Hommes et al. (2004) use ExpE to calibrate agents. They fit subjects’ forecasting behavior using a class of linear models with lags in prices and expected prices. They find that prices differ significantly from fundamental values; they exhibit oscillations around, or slow convergence to the fundamental value. Another result is that simple forecasting rules are sufficient to characterize subjects’ behavior. As the second method is considerably more complex, it can scarcely be found in the literature. One example can be found in Arifovic et al. (2006), who report on the design of a Turing tournament and its initial implementation to learning in repeated 2-person games. The objectives were to find learning algorithms that closely simulate human behavior, to find algorithms that distinguish accurately between humans and machines, and to show how to implement this methodology for evaluating models of human behavior.

  • Replication of human subject experiments with extended periods of interaction and number of agents (topic 5): experiments can be costly and difficult to extend beyond a certain parameter space. In response, an ABM could compensate for shortcomings and enable the adjustment of conditions of the system under study, observing outcomes for different distributions of agents’ preferences and different sets of parameter values over extended decision periods. Boero et al. (2010) test how reputation can improve the exploratory capabilities of agents in uncertain environments. In a laboratory experiment, subjects were asked to take investment decisions. ABM based on the observed behavioral patterns replicated the experiment exactly.

  • Investigation of the unintended effects of human subjects’ behaviors (topic 8): the focus of this topic is the exploration of the micro-macro relations based on the interactions between the individuals’ behavior and the whole economic system. This is a difficult issue to tackle using only experimental economics. The experimenters face strong time and money constraints when trying to build an experiment to represent a wide economic world. Furthermore, exploring all the relationships between individuals’ behaviors and macro features of the economy is like trying to empty the ocean with a spoon. Eliasson (1991) uses a micro-to-macro model (calibrated using business firm data) to explain how complex economic behavior emerges from the interactions of bounded rational agents. The model explains why it is difficult to predict the reactions of the economy to policies, as numerous non-linearities arise.

  • Using bounded rational consumption behavior inspired by the literature on experimental psychology, Ciarli et al. (2010) model the micro-economic behavior of firms in the final good and capital sectors and the evolution of classes of workers/consumers. They observe and explain the interactions between technological change, firm organization, income distribution, consumption behavior and growth, underlining the micro-economic sources of these structural changes.

24Broadly speaking, there are strong incentives to combine simulation modeling with empirical methods. Experimental economics and agent-based modeling share the same basis. Both enable researchers to go beyond the assumption of the homo-economicus individual, and to endorse the heterogeneity and bounded rationality of subjects or agents. Together, they form a powerful technique to understand and disentangle the complexities underlying social phenomena (Dal Forno and Merlone, 2004; Duffy, 2006; Janssen and Ahn, 2006).

2.3 Coupled Human and Natural Systems

25The ACE approach is widely used in agricultural economics and helps to model land use. As far as we know, the first article using agent-based simulation in relation to land use is that of Lansing and Kremer (1993), which models irrigation systems in Indonesia.

26Simulation modelling in agricultural economics dates back to the pioneering work of Richard Day and Theodor Heidhues in the 1960s, when the first linear programming models were developed for policy analysis. As the outcome in agricultural economics is largely influenced by uncertain variables (climate, rare events, etc.), agents are often assumed to have bounded rationality, deviating from the equilibrium of neoclassical economics (Berger and Troost, 2012).

  • 8 See Matthews et al. (2007) for a review of the wider use of this class of ABM.
  • 9 See Parker et al. (2003) and An (2012) for reviews of how human decisions are modeled in coupled hu (...)
  • 10 See Filatova et al. (2013) for a review of agent-based models in the field of coupled socio-ecologi (...)

27This class of models generally couples a cellular component representing a landscape with an agent-based component representing human decision-making. The aim is to fully integrate economic and ecological constraints.8 It should be noted that most of the time, human decisions in agent-based models of land use are simulated, based on economic theories such as the rational agent and largely ignoring other relevant disciplines, such as psychology or sociology (Groeneveld et al., 2017).9 The impacts of various governmental policies on the adoption of new agricultural practices and the structure of the farm economy are the main objects of study. These models are often designed as a tool for policymakers, with the aim of answering different public policy issues. Polhill et al. (2001) explore strategies of land use through a simulation model of rural land use, and they explain how the relative advantages of imitative and non-imitative approaches to land use selection can vary under different circumstances. Their article shows that the success of “imitation” has a complex dependence on the type of imitation used, the strategies of other agents with whom the imitator interacts, and aspects of the heterogeneity of the environment. The impact of policy changes is also a common subject. Happe et al. (2006) combine agent-based modeling of structural change with agricultural policy analysis to analyze, under various framework conditions, the impact on structural change of a regime switch in agricultural policy. They show how the effects of policies are sensitive to interest rates, managerial abilities and technical change. Consequently, the isolated analysis of a policy regime switch would be of little value for policy advice. ABMs are also used to assess policy options concerning the diffusion of innovations and changes in resource use (Berger, 2001). They evaluate the impact of different strategies for the reduction of pesticide use (Grovermann et al., 2015; Grovermann et al., 2017) and compare different policy interventions and regulations in terms of their impact on pesticide use, farm incomes and land use.10 Climate change is a growing worldwide concern, and agent-based modelling has recently been used to study the effects of climate adaptation and mitigation options in agriculture. The ABM approach is suitable to study complex environmental problems, while it allows to evaluate the socio-economic implications of climate change (Moss et al., 2001). Berger and Troost (2014) discuss the specific insights ABMs can provide in the endeavor to develop robust policies and land-use strategies in response to climate change. They show that ABMs are well-suited for uncertainty analysis. The attractiveness of the ABM approach is further reinforced by the fact that integrated assessment models tend to underestimate the potential damage caused by climate change, as well as underestimating the benefits of a transition to low-carbon growth, whereas agent-based models give a more accurate picture (Stern, 2016). Agent-based modelling allows for case studies: Troost and Berger (2014) analyze farm-level climate change adaptation in a mountainous area of southwest Germany. They demonstrate that shifting time slots for crop management can have a significant effect on agricultural supply and income, and they conclude that farm-level models can contribute to a process-based analysis of adaptation to climate change. ABM also allows for more general studies: Lamperti et al. (2018a) present an agent-based model for the study of coupled economic and climate dynamics that endogenously co-evolve across a range of different scenarii, with the aim of providing a test-bed for various combinations of macroeconomic, industrial and climate policies.

3. ACE and Statistical Physics (Econophysics)

“Imagine how hard physics would be if atoms could think” (Murray Gell-Mann).

28The literature is replete with examples of famous physicists interested in economics or finance. Remember the unsuccessful predictions of stock prices by Isaac Newton, and his consequent loss of 20,000 pounds in the South Sea Bubble in 1720, or the successful management by Carl Friedrich Gauss of the Göttingen fund for professors’ widows (Chancellor, 2000). We can also recall Louis Bachelier’s modelling of Brownian motion and formulation of what is now called the Chapman-Kolmogorov condition for Markovian processes in his Theory of Speculation, based on the observation of price movements on the Paris stock market. It has been decades now since physicists started using their tools to study collective phenomena emerging from the interactions of individuals as elementary units in social structures. Applied to economics, this gave birth to an interdisciplinary field now called econophysics (Castellano et al., 2009).

29Econophysics represents a paradigm shift from neoclassical economic thinking. It is not a new econometric approach involving the application of physics in economic studies, but rather a sub-field of physics scientifically different from economics (Jakimowicz, 2018).

30The term econophysics first appeared in 1996 in Stanley et al. (1996). The authors discuss the possibility that the behavior of large numbers of humans (as measured by economic indices, for example) might conform to scaling laws that have proved useful in describing systems composed of large numbers of inanimate objects. Using concepts and methods drawn from statistical physics to analyze socio-economic problems was soon considered by most physicists as a new field of physics. These approaches have been particularly powerful in analyzing the behavior of financial markets, as explained in section 4. Historically speaking, econophysics was stimulated by the sudden availability of large amounts of financial data that were hard to study using traditional methods of analysis. The recent crises have underlined the need for other paradigms than the traditional chartist fundamentalist approach.

31It is not easy to give a proper definition of econophysics, based on its own nature, as it is used to describe what physicists do in the field of economics. Some physicists claim that econophysics may provide an alternative theoretical framework for a new economic science. The precise characterizations of stock market fluctuations have already made a decisive mark in financial economics. The contributions of physicists are also important in the study of multi-agent iterative (and collective) learning game models for efficient resource sharing, as well as both binary- and multi-choice iterative learning games, providing a dynamic alternative to cooperative game theory.

32The availability of new large databases mentioned earlier, together with the appearance of new social phenomena caused by the emergence of Internet, has nurtured this movement. Tools and models issued from statistical physics are numerous and reviewing them is beyond the scope of this article. In what follows, we only focus on methods closely linked to ABM.

33Note that while not part of statistical physics, ABMs themselves are considered by some researchers as an econophysics tool. The ABM approach was already used in physics in the 1950s to study molecular dynamics (Alder and Wainwright, 1957) or for the creation of Monte Carlo integrations over configuration space to study statistical mechanical problems which are not analytically solvable (Metropolis et al., 1953). Statistical physics can be used in conjunction with ABM to study economic systems (Nadal et al., 2003), or to analyze agent-based models themselves (Gualdi et al., 2015).

34Chakraborti et al. (2015) review a broad spectrum of multi-agent models of competition and present the methods used for analytical analysis. Their article emphasizes the power of concepts and tools taken from statistical mechanics for understanding and explaining collective phenomena such as phase transitions and long memory, or the mapping between agent heterogeneity and physical disorder. The tools drawn from statistical physics and closely linked to ABM are used to find (or approximate) analytical results for agent-based models. We will now present these different tools and their role in helping to explain the functioning of socio-economic systems.

3.1 Mean Field Theory

35Mean field theory studies the behavior of high-dimensional random (stochastic) models by analysing a simpler model that approximates the original by averaging over degrees of freedom. Mean-field approximations were introduced in physics in the early 1900s through the work of Weiss on magnetism (Weiss, 1907).

36Slanina (2001) solve a mean-field variant of the model of a limit order driven market introduced by Maslov (2000). The agent-based model is simple: the traders can either trade at the market price or place a limit order, i.e., an instruction to buy (sell) a certain amount of the stock if its price goes below (above) a predefined level. The choice between these two options is purely random. The analytical results are slightly different from those obtained by simulation. A similar study can be found in Smith et al. (2003). The article by Izquierdo and Izquierdo (2013) illustrates how a deterministic approximation of a stochastic process can be usefully applied to analyze the dynamics of many simple simulation models and shows the relation between mean fields theory and Markov chains.

3.2 Markov Chains

  • 11 A guide to Markov chain approaches was recently published by Gagniuc (2017).

37Markov chains are stochastic models describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event.11

38Markov chains are an important tool for analyzing agent-based models (Banisch, 2015; Galán et al., 2009; Galan and Izquierdo, 2005; Izquierdo et al., 2009) and are frequently used to study dynamic systems (Bai and Wang, 2011). Their first use in economics can be traced to the 1950s (Solow, 1951) and they help to address different economic issues, such as economic evaluation in the health sector (Briggs and Sculpher, 1998), the evolution of the financial sector (Bhar and Hamori, 2004) or macroeconomic indices (Fingleton, 1997).

39Markov chains are closely linked to ABM and are viewed as an alternative methodology for studying nonlinear systems with path dependency. The unpredictability inherent to path dependency comes from the fact that, as the process unfolds, the outcome distribution changes—that is, the likelihood of obtaining a certain outcome varies with time. This is because path dependency is a property of processes similar to non-ergodic Markov chains (Vergne and Durand, 2010). Note that this analytical framework is not adapted to models including complex interactions.

40Markov chains help to analyze systems that satisfy the Markov property: a stochastic dynamic system satisfies the Markov property if the conditional probability distribution of future states of the system at any time is independent of the (past) behavior of the system. In this case, knowing the past history about how the system reached the present state does not provide any additional information about the future evolution of the system.

41Gintis (2013) presents a Markov process model of a market economy with decentralized production, consumption, and trade in many goods. He finds that such economies have stationary distributions close to market-clearing Walrasian equilibrium, with significant short-run excursions away from equilibrium generated by the inherent stochasticity of the Markov process. This article highlights the fact that agent-based models of social processes can generally be treated as finite Markov processes with analytically determined stationary distributions. This is also the case for articles by Cont et al. (2010), and Cont and De Larrard (2013). The authors model a limit order book as a continuous-time Markov process that tracks the number of limit orders at each price level in the book. The aim is to strike a balance between three desirable features: easy calibration to high-frequency data, reproduction of various empirical features of order books and analytical tractability.

3.3 Kinetic Wealth Exchange Models

  • 12 The fundamental law of equilibrium statistical mechanics whereby the probability distribution of en (...)
  • 13 See Yakovenko and Rosser Jr (2009) or Goswami and Chakraborti (2015) for literature reviews on this (...)

42This method is based on the kinetic theory of gases, which describes a gas as a large number of submicroscopic particles, all of which are in constant, rapid, random motion. Randomness arises from the many collisions of these particles with each other and with the walls of the container. The objective is to explain the macroscopic properties of such systems (pressure, temperature, etc.). In econophysics, individuals are analyzed as particles, and the models seek to predict the evolution of the distribution of a quantitative variable (like wealth, for example). The rules of wealth exchange are simplified, based on the assumption that the average behavior can be described simply and will be representative. Dragulescu and Yakovenko (2000) argue that money is a conserved quantity in a closed economic system, and thus, by analogy with energy, the equilibrium probability distribution of money must follow the exponential Boltzmann-Gibbs law.12 Several articles using this approach can be found in economic literature. Molico (2006) shows that money can be considered as neutral if changes in the money supply are accomplished via proportional transfers. Lagos and Wright (2005) propose a new framework, based on explicit micro foundations, within which macro policy can be studied. These models can be generalized by introducing heterogeneity in agents (Angle, 2002).13

3.4 Master Equations

  • 14 See the recent book by Di Guilmi, Gallegati, and Landini (2017) for an introduction to the methods (...)

43This method was introduced to economics (Weidlich and Braun, 1992) from physics (Haake, 1973). Master equations are differential equations that describe the evolution of the probabilities of Markov processes for systems that switch between states, where the switching (in continuous time) is determined by a transition rate matrix. They can be considered as a continuous time version of the recurrence relations for Markov chains. It is often impossible to solve a master equation. However, it is possible to obtain easily approximated equations for the first moments of the probability using mean field theory. This has given rise in economics to what are called analytically solvable heterogeneous interacting agent (ASHIA) models, which aim to study systems of interacting heterogeneous agents without using numerical simulations (Di Guilmi et al., 2012).The idea is to introduce a level of aggregation obtained by screening the agents through clustering. The dynamics of the population of individuals in each cluster also defines the evolution of the whole economy.14

4. Agent-Based Modeling of Markets

  • 15 As defined by Akerlof in his pioneering article “The Market for Lemons”, published in 1970 in The Q (...)

44Heterogeneity of goods and agents, limitation of information and social interactions are particularly present on certain markets. When the quality of goods is uncertain or difficult to evaluate, the influence of social phenomena on the market outcome, increases. The representation of markets through the crossing of aggregate demand and supply of a homogeneous good has dwindled. If industrial organization modeling has increased our understanding of some particular markets, its modeling neglects the importance of social phenomena. The modeling of signals of quality and imperfect information help to better design individual choices. Nevertheless, exchange markets still present particular features not explainable through this paradigm. We choose here to describe how ABM help to better understand the functioning of three particular types of markets, namely financial markets, housing markets and fish markets. At first glance, this choice may seem surprising. However, these three markets can be analyzed as exchange markets with low or no “production costs”. Signals of quality15 are not common knowledge and information is private. The evaluation of the goods depends on the objective characteristics of the dwelling but also on the social attractiveness of the geographic area (housing markets), on the ability of agents to compress information and the influence of their social group (financial markets), on specific economic characteristics but also on social relationships (fish markets). As mentioned in section 3, physicists have been interested in economic phenomena for some time. They have developed useful methods to analyze different market behaviors. Their contributions are exceptionally significant in the area of financial markets and housing markets, as we explain in subsections 4.1 and 4.2. The different contributions bring new insights to a more general discussion concerning the efficiency of market structures. Is it pertinent to sell a perishable good through the same market mechanism as a house or an asset? How do agent interactions influence the formation of prices?

4.1 Housing Markets

4.1.1 ACE for Realistic Urban Models

45Meen and Meen (2003) note that modeling an urban housing market needs to integrate the specific characteristics of urban markets, in particular the importance of social attractiveness, non-linearity and segregation. They examine how empirical models of urban housing markets might be constructed as a basis for policy analysis. A model is presented, whose output is compared to empirical data. Non-linearities consistent with recent work on thresholds in local housing markets can be observed. Simple cellular automata are also used to demonstrate this point and explain how segregation may arise. They conclude on the need for policy makers to gain access to usable urban housing models. Since Meen and Meen’s call for usable urban housing models, urban land-use modeling methods have enjoyed substantial improvements. As Huang et al. (2014) note, agent-based modeling provides more sophisticated urban land-use models and can help to address the challenges faced by traditional models. To offer a retrospective on the developments in agent-based models of urban residential choices, these authors review fifty-one relevant models and classify them into three general categories: i) urban land-use models based on classical theories, ii) different stages of the urbanization process and iii) integrated agent-based and microsimulation models. As a positive point for agent-based urban land-use modeling, these authors note fundamental new features introduced by ACE, as the possibility of including heterogeneity in agents’ attributes and behaviors. Another positive feature is the representation of land-market processes, namely the combination of agents’ preferences, resource constraints, competitive bidding, and endogenous relocation. They conclude that, by modeling agent heterogeneity and land markets, and by exploiting a much broader dimension of output, our better understanding of urban land-use change will improve the fitness and robustness of models.

4.1.2. ACE to Explain the Emergence of Segregation

46Spatial econometrics and the methodology of hedonic prices allow to estimate the prices of the different objective characteristics of a dwelling. However, these methods fail in measuring the influence of mimetism or social attractiveness and then the emergence of social segregation.

47In 1969, Thomas C. Schelling developed a simple but striking model of segregation. It shows how local interactions can lead to surprising aggregate structures. His microeconomic model explains how an integrated city could unravel to a rather segregated city, notwithstanding relatively mild assumptions concerning the individual agents’ preferences, i.e., where no agent prefer the resulting segregation. This model, designed when computers were of no help, has been largely extended. ACE now allows us to understand how micro decisions structure the socio-economic space. It explains how segregation emerges according to the social preferences of agents (Vinkovic and Kirman, 2009), or to the influence of market design on individuals’ choices (Gauvin et al., 2013; Pangallo et al., 2019). Pancs and Vriend (2007) examine the robustness of Schelling’s model, focusing on the individual preferences as driving force. In a certain sense, their results are more pessimistic than Schelling’s. They show that even if all agents have a strict preference for perfect integration, best-response dynamics may lead to segregation. They cast doubt on the ability of public policies to generate integration—for example, through the promotion of openness and tolerance with respect to diversity. Vinkovic and Kirman (2009) use the physics of clustering to sophisticate Schelling’s model of segregation. The economic concept of utility is replaced by the physics concept of a particle’s internal energy. Their results are in line with those of Pancs and Vriend (2007). The resulting segregated areas can be very large and behave like spherical liquid droplets or like a collection of static frozen clusters. This model aims to provide a useful framework for studying many spatial economic phenomena involving individuals making location choices as a function of the characteristics and choices of their neighbors.

48The importance of others’ choices is also considered in studies by Gauvin et al. (2013) and Pangallo et al. (2019). These two articles propose more sophisticated models than the previous ones and underline the possibility of social diversity, under precise conditions. What is modeled is an exchange market, and agents are designed by both social preferences and budget constraints. Gauvin et al. (2013) introduce a decentralized model of housing transactions between agents who are heterogeneous in their willingness to pay. Exchanges are bilateral and prices result from a bargaining process. A key assumption is that agents’ preferences for a location depend on both the intrinsic attractiveness and the social characteristics of the neighborhood. An agent-based model is simulated but the stationary space distribution of income is analytically and numerically characterized. The main results are that socio-spatial segregation occurs if and only if the social influence is strong enough, but even so, some social diversity is preserved at most locations. Comparison with data on the Paris housing market shows that the results reproduce general trends of price distribution and spatial income segregation.

49Pangallo et al. (2019) represent the functioning of a continuous double auction housing market and study the relation between income segregation, income inequality and house prices. Unlike most of the traditional models in urban economics, the behavior of buyers and sellers is specified, together with the price formation mechanism. Buyers who differ by income select among heterogeneous neighborhoods using a probabilistic model of residential choice; for an agent, the quality of the neighborhood depends on social attractiveness, which depends on the choices of other agents. Sellers employ an aspiration level heuristic to set their reservation offer price. The simulation of the agent-based model brings to light the facts that i) a more unequal income distribution lowers prices globally, but implies stronger segregation; ii) a spike in demand in one part of the city increases the prices all over the city; iii) subsidies are more efficient than taxes in fostering social mixing.

4.1.3 ABMs as Policy Tools

50The agent-based modeling of housing markets has been seen as a useful tool for policy makers. As the preservation of social diversity in big cities is a hot political topic, a large number of articles investigate the functioning of housing markets and the main factors of influence. Agent-based models have been used to analyze the dynamics of housing markets in China (Zhang et al., 2013; Zhang and Li, 2014), the United States and the United Kingdom. Institutions like the Bank of England have applied them to better understand residential dynamics in large urban areas. Baptista et al. (2016) study the impact of macro prudential policies on key indicators of the UK housing market. They develop an agent-based model which addresses heterogeneity by modeling the individual behaviour and interactions of first-time buyers, homeowners, buy-to-let investors, and renters at a micro level. They then observe the resulting aggregate dynamics in the property and credit markets. Their model is calibrated thanks to a large selection of micro-data from diverse sources. The main results suggest that an increase in the size of the buy-to-let sector may amplify house price cycles and increase house price volatility. In a second step, they implement a loan-to-income portfolio limit, in order to evaluate the effect of macro prudential policies on several housing market indicators. They find that this policy attenuates the house price cycle. The links between housing and financial markets are important. The 2008 crisis was a reminder that the housing market strongly depends on the financial market. Geanakoplos et al. (2012) affirm that systemic risk must include the housing market, though economists have generally neglected it. These authors built an agent-based model of the housing market based on twenty years of individual data from Washington, DC. First results suggest that the housing boom and bust of 1997-2007 was due in large part to changes in leverage rather than interest rates.

4.2 Financial Institutions

“Those of us who have looked to the self-interest of lending institutions to protect shareholders’ equity (myself especially) are in a state of shocked disbelief. Such counter-party surveillance is a central pillar of our financial markets’ state of balance. If it fails, as occurred this year, market stability is undermined. ... The whole intellectual edifice, however, collapsed in the summer of last year.” (Alan Greenspan, 2008)

4.2.1 ACE as a Response to the 2008 Crisis

51The financial crisis of 2007–2008 had an important impact in the macroeconomic field, showing the need for new methodologies as DGSE models failed to anticipate the imminence of the recession: they gave no indication of any form that a crisis was coming. Furthermore, the exogenous shock process does not give sufficient information regarding the specific causes and sources of shocks; they must be made endogenous. This led a number of famous economists to assert that the 2008 economic crisis was a crisis for economic theory (Kirman, 2010, 2016; Krugman, 2011; Stiglitz, 2011; Delong, 2011). They announced the need to develop new models of markets as better tools for decision-makers. An extensive ABM literature followed, analyzing the functioning of financial markets and the behavior of bank networks. Buchanan’s article (2009) is a plea for agent-based computational economics. It describes mainstream economics as capable of providing good insights into human behavior as long as it assumes that it will lead to a stable self-regulating market, with prices never departing too far from the equilibrium. But in a time of crisis, the behavior of financial markets can only be described as chaotic, and certainly not stable. Buchanan then promotes agent-based models as they make only minimal assumptions about human behavior or inherent market stability.

52In an article published in Nature, Farmer and Foley (2009, 2), note that:

The best models they have are of two types, both with fatal flaws. Type one is econometric: empirical statistical models that are fitted to past data. These successfully forecast a few quarters ahead as long as things stay more or less the same, but fail in the face of great change. Type two goes by the name of 'dynamic stochastic general equilibrium'. These models assume a perfect world, and by their very nature rule out crises of the type we are experiencing now.

As a result, economic policy-makers are basing their decisions on common sense, and on anecdotal analogies to previous crises such as Japan’s 'lost decade' or the Great Depression... The leaders of the world are flying the economy by the seat of their pants.

This is hard for most non-economists to believe. Aren’t people on Wall Street using fancy mathematical models? Yes, but for a completely different purpose: modeling the potential profit and risk of individual trades. There is no attempt to assemble the pieces and understand the behaviour of the whole economic system.

53This recent trend to rethink economic methodology in the aftermath of the subprime financial crisis was largely explored by Bouchaud (2008). The 2008 financial crisis highlights the crucial need for financial market analysts to move away from dogmatic axioms and focus on data, orders of magnitude, and the understanding of agents’ behaviors. ACE allows to take into account the highly distributed nature of trading in financial markets, and to model them as evolving systems of autonomous, interacting agents (Buchanan, 2009). Going beyond the binary vision of fundamentalists and chartists, ACE can model complex interactions and test the implications of the disposition effect (avoiding regret) on investors’ interactions and price setting. Agent-based models help to understand potential vulnerabilities and paths through which risks can propagate across the financial system (Bookstaber, 2012). Pruna et al. (2017) drive an agent-based model able to match the widely observed properties of financial assets. The implications of various empirically observed heuristics are evaluated, associated with the observed behaviors of investors. It then presents a new behavioral asset pricing model with heterogeneous agents. When loss aversion is introduced, as a new behavioral bias, the agents’ interactions completely change. The resulting dynamics replicates a rich set of the stylized facts of financial data: conditional heavy tails of returns, gain/loss asymmetry, volume power-law and long memory and volume-volatility relations. Colander et al. (2008) defend a similar idea, that macroeconomics should move beyond representative agent DSGE models and focus on alternative heterogeneous agent macro models that are more capable of taking into account agent interactions, complexity, coordination problems and endogenous learning. The DGSE models have improved since then, but these improvements are described by Fagiolo and Roventini (2016) as a “Ptolemaic exercise”. Nevertheless, introducing heterogeneous agents or substituting the rationality assumption with insights drawn from behavioral economics could substantially change the working of DSGE models (Le Baron, 2006; Akerlof, 2007; Sinitskaya and Tesfatsion, 2015).

4.2.2 ABM Helps to Determine Stability Conditions

54Policy makers needs explanations to the (in)stability of financial markets. Bookstaber et al. (2018) simulate an agent-based model to analyze the vulnerability of the financial system. Their model focuses on the intermediation functions of the bank/dealers in order to trace the path of shocks that come from sudden price declines, as well as shocks that come from the various agents. The model demonstrates that it is the reaction to initial losses rather than the losses themselves that determine the extent of a crisis. It argues that ABM is a sound methodology to study risk management, as it can replicate the propagation of key crisis dynamics such as fire sales and funding runs. The structure of the banking network can also be a factor of instability. Chan-Lau (2017) presents an agent-based model for analyzing the risk in a banking system in which banks’ business decisions drive the endogenous formation of interbank networks. This platform serves to illustrate the effect of changes on regulatory requirements, solvency, liquidity, and interconnectedness risk.

55As the 2008 crisis demonstrated, the potential impact of interconnected financial institutions on inter-bank financial systems is a major financial stability concern for central banks and regulators. The ACE method can prove useful to tackle this problem, by focusing on system dynamics. Serri, Caldarelli, and Cimini (2016) build an agent-based model of 183 European banks that were publicly traded between 2004 and 2013. Their analysis points to the key role played by the speed of the crisis outbreak, which sets the maximum delay for central authorities’ intervention to be effective. Liu et al. (2017) use ABM to examine how financial shocks propagate through contagion effects. The authors argue that endogenous individual bank choices are needed to correctly model how losses develop as the interbank lending network evolves. Results are compared to those of a traditional stationary network for contagion. The model is able to reproduce dynamics similar to those of the 2007-09 financial crisis. When calibrated to post-crisis data from 2011-14, the model shows how the U.S. banking system has reduced its likelihood of bank failures through network contagion and illiquidity, given a similar stress scenario.

4.2.3 ABMs as Behavioral Models

  • 16 The Red Queen principle refers to an effect of competitive co-evolution between species.

56Agents’ behavior on financial markets has long been a focus of ACE, as this approach can take heterogeneous behaviors into account. Martinez-Jaramillo and Tsang (2009) study the behavior of stock markets through an artificial financial market. Technical (sophisticated genetic programming of agents that co-evolve), fundamental and noise traders are simulated. The authors investigate the conditions under which the statistical properties of an artificial stock market fit those of the real financial markets. Moreover, they model the pressure to beat the market by means of a behavioural constraint imposed on the agents related to the Red Queen principle in evolution.16 They investigate the effect of such a constraint on the price dynamics and the wealth distribution of the agents after several periods of trading, in the different simulation cases. They demonstrate how evolutionary computation plays a key role in studying stock markets.

57An important issue for modelers is the opportunity to access to empirical data to model agent behavior. Aloud et al. (2015) use ACE approach to model trading behavior in the foreign exchange market. They establish statistical properties (stylized facts) of the traders’ behavior in this market using a high-frequency dataset of individual traders’ historical transactions on an account level spanning 2.25 years. Then they compare the collective behavior of the real and artificial agents.

  • 17 The value at which they expect the price to stop rising and start falling.

58Lee and Lee (2015) develop an agent-based model to replicate financial instability, such as bubbles and crashes in asset markets, by introducing a simple idea of heterogeneous expectation and herding behavior by which agents in different groups have different expectations about a tipping point.17 The authors show that when agents have different expectations about the tipping point, the collapse of the price does not emerge automatically, and price fluctuations can be small. The more agents share the same expectations about the tipping point, the higher the volatility of the asset price.

59While ABM serves to study the dynamics of financial crisis, they are also used to test for the potential effect of regulation on financial markets, in order to prevent further crisis. Yagi et al. (2010) discuss the effectiveness of short-selling regulations using artificial markets as an agent-based model of financial markets. They show that short-term regulation contributes to market stability whereas long-term regulation inhibits it. Comparing the price variations between the market where short-selling was regulated and the one where it was not regulated, they find that the former rebounded faster than the latter.

60Yeh and Yang (2010) propose an agent-based framework to examine the effectiveness of price limits in an artificial stock market. The simulated market is composed of different boundedly rational traders for whom learning behavior is represented by a genetic programming algorithm. Empirical data is used to calibrate the model. An original result is that imposition of price limits is shown to possess both positive and negative effects. However, compared with a market without price limits, appropriate price limits help to reduce volatility and price distortion, and increase the liquidity and welfare.

61High-frequency trading (HFT) is responsible for what are now called flash crashes. Leal and Napoletano (2017) investigate the effect of a set of regulatory policies aimed at HFT. They build an agent-based model of a limit order book, able to generate flash crashes as the result of the interactions between low- and high-frequency traders. The impact of the imposition of minimum resting times, circuit breakers, cancellation fees and transaction taxes on asset price volatility and on the occurrence and duration of flash crashes are detailed. Monte-Carlo simulations reveal that HFT-targeted policies imply a trade-off between market stability and resilience. Policies able to tackle volatility and flash crashes also hinder the market from quickly recovering after a crash. This result is mainly due to the dual role of HFT, as both a cause of flash crashes and a key player in the post-crash recovery.

62The literature is very rich and even a short review is way beyond the scope of this article. The interested reader will find a recent overview of the literature in a book written by Bargigli et al. (2017).

4.3 Fish Markets

63The use of agent-based models for the analysis of housing markets or financial markets is standard. Sections 4.1 and 4.2 have underlined the need to model heterogeneity and the interest of simulating different institutional environments. The use of agent-based models for the study of fish markets is maybe less usual. Fish markets represent a setting where goods are heterogeneous in quality and information is asymmetric. A crucial issue for the buyers is to evaluate the quality of the good they wish to consume. The empirical analysis of fish markets always reveals strong price dispersion for homogeneous or very similar goods. This has been observed in the past by various economists, including Thornton, Marshall and Pareto. One important reason is that fish is a highly perishable good and the quality decreases rapidly. Today, due to environmental constraints, fish is becoming a scarce resource and buyers have to develop strategies. As food markets, the behavior of fish markets influences the level of food security and highly volatile prices have negative effects. In what follows, we explain how agent-based models can improve our understanding of the functioning of fish markets.

4.3.1 Heterogeneity and Scarcity

64As far as we know, the first article to use ABM to depict a wholesale fish market was written by Kirman and Vriend (2001). The objective of the authors was to explain two paradoxical stylized facts of that market, i.e., high loyalty of some buyers to sellers, and persistent price dispersion. Buyers learn to become loyal as sellers learn to offer higher utility to loyal buyers, while these sellers, in turn, learn to offer higher utility to loyal buyers as they happen to make higher gross revenues from them. The model also explains the effect of buyer heterogeneity.

65On fish markets, not only are the buyers and sellers heterogeneous, but so are the products. Heterogeneous goods and a lack of quality signals have been shown to have a strong impact on price formation. Gobillon et al. (2016) develop an extension of the traditional hedonic price specification, able to take into account the unobserved heterogeneity of sellers, buyers and seller–buyer matches. Their estimation is driven on a dataset containing information from different French wholesale fish markets. Results show that unobserved heterogeneity plays a significant role in price setting. Wamukota et al. (2015) examine how selected socioeconomic characteristics of fishers and traders shape market prices at five coastal communities in Kenya. The link between individual characteristics, market prices, and the outcomes of such interactions is shown to be more complicated than commonly perceived. In most cases, fish markets are daily and local markets. People know each other and social interactions matter. ABM is a good tool to study market designs where people interact, information is limited and pricing is strategic (Mignot et al., 2012).

66A specific characteristic of fish markets is that fishing is a gathering activity, and that stocks are plummeting. The supply of fish is decreasing and will probably continue to decrease. 40% of seafood is now traded internationally and many marine species suffer from overharvesting (Elsler et al., 2019). As a consequence, price and market structures in fisheries change rapidly, and are associated with the emergence of export markets, increasing globalization of supply chains, and the dynamics between local supply and global market demand. This scarcity of fish is becoming a major problem, a problem often tackled by the introduction of fishing quotas. Bellanger et al. (2017) develop an individual-based bio-economic model, applied to the Bay of Biscay sole fishery, to investigate alternative quota management systems. The effectiveness of governance scenarios is discussed with regard to the challenge of capacity adjustment.
Elsler et al. (2019) present a bio-economic fishery model, to analyze the effect of transitioning between markets on the (over)exploitation of species and the stability of income. It is shown that transition management needs to account for non-linear price changes, since earlier policies may not be suitable after globalization.

4.3.2 ABM for a Better Understanding of New Market Designs

67The rarefaction of fishery resources pushed international institutions to reorganize the architecture of markets, to improve the management of fish stocks. These new market designs were also considered more efficient, while functioning through different auction systems. These new forms of markets have often been rejected by the different agents, both fishmongers and fishermen. The European Commission and the French Ministry of Agriculture have then been forced to accept surprising market organizations such as the one found in Boulogne-Sur-Mer. On this market, goods can be sold either through bilateral exchanges or through auctions. This organization is stable over time and this sounds like an economic paradox (we would expect one form of exchange to become dominant). First stylized facts reveal that sellers adopt different strategies: they can be loyal to one particular market (negotiated or auctions) but most of the time, they switch regularly from one form of organization to the other. To explain this surprising phenomenon, Mignot et al. (2012) build an agent-based model where agents revise their strategies according to what they observe, in terms of market price and quantities. The information is imperfect, depending on the individual matching. The agents exchange after having matched. The conditions under which the results on the artificial market match the real market empirical evidence are then calculated. Because all the myopic agents revise their strategies at the same time, switching is a stable strategy.

68The question of market power when it comes to perishable goods is an important one. It is commonly admitted that sellers are typically in a weak bargaining position, since perishable products cannot be stored for long without losing their value. Miyashita (2017) build ABMs to test market designs aimed at resolving this asymmetry between buyers and sellers. But Mignot and Vignes (2018) show that in a context of dwindling resources, market power can switch to the seller side.

69As it is the case for other markets like financial markets, characterization of the behavior of market participants is also an important issue. As quality signals are scarce, buyer-seller relationships are used to substitute trust for observation of quality.

70Gallegati et al. (2011) drive a data analysis on the Ancona fish market and show how buyer-seller relationships are less important on an auction market than in a pairwise bargaining market: they also find that a significant amount of loyalty is still present under the auction mechanism. Through an agent-based model, Moulet and Rouchier (2008) investigate the formation of prices in a perishable goods market where agents bargain repeatedly through pairwise interactions. This paper is focused on two aspects that seem important to the agents of this market: the passage of time and the update in judgment when gathering information. An agent-based model is built that reproduces the main features of the data on the dynamics of offers, transaction prices and agents’ behavior during the bargaining phases.

5. Conclusion

71The increasing popularity of ACE in different fields of applied economics corresponds to a change of perspective in the forma mentis of scientists. Traditional economics is based on a reductionist approach according to which, if you know the basic elements of a system, you can predict its behavior and properties. Agent-based computational economics has been developed in parallel with other alternative methods such as econometrics or experimental economics. This article brings to light how these different techniques can be used in a complementary way, both to simulate models with boundedly-rational agents and to improve the robustness of the results. While the neo-classical paradigm proposes complicated dynamic optimization schemes for representative agents, ACE allows to explore the patterns that may emerge from aggregation over heterogeneous individuals, who make simpler but still coherent calculations. To this end, ACE uses a bottom-up approach that does not need strong assumptions regarding individual behavior to obtain a tractable aggregation, allowing modelers to include more realistic behavioral rules in the aggregation, such as learning, coordination and interactions. ABMs generate data describing heterogeneous individuals and the robustness of results can be checked through the estimation of econometric tests on this simulated data. The goal of experimental economics is to investigate individual behavior and the emergence of aggregate regularities through analysis of human subject experiments. ABMs can then be run, with sophisticated behavioral rules determined from the results of the experiments.

72The study of socioeconomic systems has attracted the interest of physicists for some time now, and this has given rise to econophysics. Their specific tools like mean field theory or Markov chains help to analyze the dynamics and path dependencies of systems. Again, combined with ABMs, they provide fruitful tools for the study of interactive heterogeneous individuals.

73ACE, experimental economics and econophysics share common foundations. Phenomena such as heterogeneity, social interactions and path dependencies have to be properly modeled, since an economic system depends on its dynamics. This article has shown how ABMs are invaluable for analyzing crucial economic problems such as the organization of markets or the efficiency of public policy. These approaches help to “open the black box of markets”. Three markets in particular have exposed the explanatory shortcomings of the orthodox paradigm, namely the housing market, the financial market and the fish market. These markets share a certain lack of efficiency (prices vary for similar goods and the possibilities of arbitrage are numerous). Their imperfections have numerous socioeconomic consequences: we need only think of the different financial crises, the large number of people living in slums or difficulties in the conservation of fishery resources. There is a need for policy tools and ABMs are capable of providing them. Econophysics has shed valuable light on the functioning of financial markets or the emergence of social segregation. Experimental economics has increased our understanding of individual behaviors and of the consequences of social interactions on the market outcome. When social interactions produce complex systems, difficult to solve analytically, computational methods can provide a set of solutions. The methodology of agent-based computational economics is useful to study the processes behind the emergence of equilibria and the general unfolding of patterns in the economy. It helps to explain how some macroeconomic phenomena can be endogenously generated by boundedly-rational, interacting agents in economic systems.

74But there is still a core set of issues that need to be addressed. A lack of theoretical models has regularly been pointed out. To that, we can add a lack of comparability between models, and the need for standard techniques to build, analyze and validate agent-based models.

The authors wish to thank Jean-Sebastien Lenfant and Francesco Sergi, the editors of this special issue of Œconomia, two anonymous referees, and the participants at the Œconomia workshop “simulations in economics” for helpful comments and discussions.

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1 See Gallegati and Kirman (2012) and Ballot, Mandel, and Vignes (2015) for detailed presentations of former models.

2 A bottom-up approach to complexity consists in deducing the macroscopic objects and their complex phenomenological ad-hoc laws in terms of a multitude of elementary microscopic objects interacting by simple fundamental laws, and ABM allows to follow the genesis of this complex macroscopic phenomenology. Macroscopic objects at a given scale can become microscopic objects at the next scale.

3 We thank one anonymous referee for providing us with this clear definition of how ABM is used.

4 See Fagiolo et al. (2017) for a recent critical review of existing validation techniques.

5 See Huang (2015) for a recent review.

6 In “experience-weighted attraction” (EWA) learning, strategies have attractions that reflect initial predispositions, are updated based on payoff experience, and determine choice probabilities according to some rule.

7 The test of an algorithm’s ability to generate behavior that an external observer cannot distinguish from human behavior.

8 See Matthews et al. (2007) for a review of the wider use of this class of ABM.

9 See Parker et al. (2003) and An (2012) for reviews of how human decisions are modeled in coupled human and natural systems.

10 See Filatova et al. (2013) for a review of agent-based models in the field of coupled socio-ecological systems.

11 A guide to Markov chain approaches was recently published by Gagniuc (2017).

12 The fundamental law of equilibrium statistical mechanics whereby the probability distribution of energy ε in a system is P(ε) = C*e^(ε/T), with T the temperature and C a normalizing constant.

13 See Yakovenko and Rosser Jr (2009) or Goswami and Chakraborti (2015) for literature reviews on this subject.

14 See the recent book by Di Guilmi, Gallegati, and Landini (2017) for an introduction to the methods and tools, together with some applications.

15 As defined by Akerlof in his pioneering article “The Market for Lemons”, published in 1970 in The Quarterly Journal of Economics.

16 The Red Queen principle refers to an effect of competitive co-evolution between species.

17 The value at which they expect the price to stop rising and start falling.

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Sylvain Mignot et Annick Vignes, « The Many Faces of Agent-Based Computational Economics: Ecology of Agents, Bottom-Up Approaches and Paradigm Shift »Œconomia, 10-2 | 2020, 189-229.

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Sylvain Mignot et Annick Vignes, « The Many Faces of Agent-Based Computational Economics: Ecology of Agents, Bottom-Up Approaches and Paradigm Shift »Œconomia [En ligne], 10-2 | 2020, mis en ligne le 01 juin 2020, consulté le 22 avril 2021. URL : ; DOI :

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Sylvain Mignot

Lille Catholic University (FGES) and Lille University (LEM, UMR 9221),

Annick Vignes


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