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Simulations in Economics: Methodological and Historical Perspectives

Agent Based Models and Complex Individuals: An Epistemological Analysis

Modélisations multi-agents et individus complexes : une analyse épistémologique
Solange Regina Marin, Brena Paula M. Fernandez et Daniel de S. Vasconcelos
p. 231-256

Résumés

La littérature sur les Agents Based Models (ABMs) semble tomber d’accord sur le fait que ces derniers pourraient remplacer le modèle néoclassique d’agent rationnel. La question est de savoir si ce nouveau modèle, réaliste et complexe, nécessite un concept d’individu tout aussi complexe. Nous proposons l’application de trois concepts majeurs de l’épistémologie des sciences sociales à la discussion sur le concept d’individu complexe : i) l’analyse situationnelle poppérienne ; ii) la rationalité limitée de Simon ; iii) le concept de causalité cumulative circulaire de Myrdal. Nous soutenons qu’il s’agit là de points de départ prometteurs pour une analyse du comportement humain, de la complexité de l’individu et des ABMs.

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1The definition of economics as a science based on rational choice is well known and widely accepted by neoclassical economics. Rational choice theory, also known as rationality theory, was developed in the twentieth century by philosophers, economists, mathematicians, and statisticians. The idea of rational decision may be applied not only in economics, but also to other disciplines, including political science, business management, public policy, international affairs, and evolutionary biology. But what does it mean to say that agents—those who act in an autonomous, self-referenced, practical oriented and objective way—do it rationally? Neither the economists’ nor the philosophers’ meaning of ‘rationality’ corresponds to the layman’s understanding of the term (Aumann, 1997).

  • 1 We use the terms “epistemology” and “epistemological analysis” in its more traditional meaning, i.e (...)

2According to the common sense, rationality means acting with good reasoning and with as much information as possible. Among philosophers, an action is generally defined as rational if an agent chooses, among all feasible options, the one most appropriate for achieving his goals, given individual’s reasoning about all the possible and contingent outcomes. In other words, in epistemological terms,1 rationality means consistently applying adequate means to achieve well-specified and desired ends. Theories that deal with rational decision, therefore, assume that agents have beliefs and desires (in the sense of targets to achieve) and that they search for expected outcomes, even when they are not conscious of the reasonableness of their actions.

3Neoclassical economics is an axiomatic theory, in which individual is the starting point of the explanations derived from the method it adopts. The axioms of neoclassical economics are given, especially the rationality principle. If an observed human action does not fit axiomatic specifications, the behavior is ruled out of theory as exogenous and/or irrelevant.

4In the last twenty years a different way of doing economics has been developed under different names: complexity economics, agent-based modeling (ABM), generative economics, and Santa Fe economics. For Arthur (2010a), a member of Santa Fe Institute, the economy, when out of equilibrium, reveals itself as not deterministic, not directly predictable, and not mechanistic, but as process-dependent, organic, and evolving. In the traditional approach, behavior in the economy is in steady state equilibrium if individuals in the economy have well-defined problems and use deductive reasoning as the basis for their actions. Complexity framework, on the other hand, understands the economy as always in process and changing, in which individuals seek to make sense of situations using whatever reasoning they have at hand, creating outcomes they must individually react to anew. The resulting economy is not a well-ordered machine, but a complex evolving system that is imperfect, continually being constructed anew, and brimming with vitality (Arthur, 2010a).

  • 2 Some contributions to this discussion are Holland (1975); Holland and Miller (1991); Bowles and Gin (...)

5The discussion of complexity and economics involves different methods of analysis and a consensus on a different notion of about basic agents (individuals) that differs from homo economicus.2 Beinhocker (2006) uses Mr. Spock (the Star Trek series character) for explaining the rational agent. Imagine that you go to a grocery and see beautiful red apples. How do you decide to buy some apples? In traditional economics, you have well-defined preferences for apples in comparison with other things you could buy. You may have well-defined preferences for things you may buy at any point in the future, yet, since the future is uncertain you assign probabilities to those potential purchases. Such well-defined preferences are ordered logically. You have a budget for apples. While you consider the apples, you make a calculation of trade-offs, and arrive at an optimal answer—to buy or not to buy. It is the Spock-like method. In Beinhocker's words, it is the perfect-rationality method resulting in action. That method goes back to Walras and Jevons, who adopted perfect rationality as an assumption in order to fit economics into the nineteenth-century equilibrium framework. This assumption was adopted not because it was a good description of real human behavior, but to make the math work in the equilibrium framework.

  • 3 The “El Farol bar problem” is a problem in game theory modelled as a static game, as follows: every (...)

6Beinhocker (2006) argues that real people are different from traditional, idealized, fully rational agents in economic theory, because they make mistakes, while the Spock-like agents do not. Our brains do not have the kind of calculating power and logical consistency needed to be perfectly rational. Besides, there are economic problems that do not have rational solution—like Brian Arthur´s Bar Problem.3 It shows that much of the volatility observed in the real-world economy may be a result of the dynamics of people’s decision rules rather than from exogenous, random shocks. Beinhocker (2006) argues that an alternative to assessing human behavior as homo economicus applies the theories of modern cognitive science. Modern cognitive science studies the software of the human mind rather than the hardware of the brain. Modern cognitive science applies inductive rationality to human behavior rather than the deductive rationality of neoclassical economics.

7Arthur (1994, 411) states that economists were uneasy with the assumption of perfect, deductive rationality in decision contexts that are complicated and ill-defined, because the level at which humans can apply perfect rationality is limited. As human beings, in these contexts we use inductive reasoning: from a variety of working hypotheses, we choose the most credible, and we develop new hypotheses when others cease to apply. Such reasoning can be modeled in a variety of ways. Usually this leads to a rich psychological world, in which one agent’s ideas or mental models compete against other agents' ideas or mental models—a world that is both evolutionary and complex.

8Beinhocker (2006) emphasizes, in the case of apples, that in the emerging complexity economics we think like this: “hmmm, apples… I will make an apple pie, prices look good,” and then we buy the apples (inductive rationality method). A new model of homo economicus describes humans as inductively rational pattern-recognizers who make decisions in ambiguous and fast-changing environments and learn over time.

  • 4 Pyka and Fagiolo (2005), for instance, states that besides the various labels under which different (...)
  • 5 The term “Methodology” is used here as well in the hole text in the philosophical sense of “an epis (...)

9The present paper focuses on Agent-Based Models (ABMs), a research field that highlights the discussion of complexity in economics.4 First, such modeling offers useful innovations for economic methodology5 regarding human interaction. Second, it presupposes a concept to model the micro-macro relationships of individuals different from the traditional rational agent used by neoclassical/Walrasian economics.

10In the beginning of the 21st century, research based on ABMs proposed that economics derive inferences from formalizations using computational math. It analyzed the economy as a complex system based on its micro foundations. These foundations are based on the interactions among heterogeneous agents under asymmetric information (Gaffard and Napoletano, 2012). More narrowly defined, this approach is called “Agent-based complexity” (Gallegati and Kirman, 2012).

11We will explore key ideas that underlie the complexity concept, inherent to the ABM. Complexity is an alternative theoretic framework within economic science based upon complexity theory and nonlinear models. Within that framework the economic environment is viewed as an open system composed of heterogeneous agents with bounded rationality. The interaction of individuals gives rise to emergent phenomena, and to a state of macro-level non-equilibrium in which the economy is in constant change due to its internal dynamics. In many important aspects, ABM economics, considered as a complex phenomenon, can be seen as a mirror inversion of neoclassical theory. Figure 1 presents the dichotomies between both paradigms. In the relevant literature, we have identified three contrasting pairs between neoclassical economics and the ABM complexity approach:

Figure 1: Dichotomies between Neoclassical and ABM Modelling

Neoclassical Modeling

ABM approach

Methodological Approach

Natural science

Social science

Agents

Substantive Rationality

Bounded Rationality

Science Model

Linear causation

Circular Cumulative Causation

Source: Elaborated by the authors.

12Davis (2017) argues that for standard economics, the economic methodology is unchanging, closed, and natural. Whereas, for ABM, economics is evolving, open, and social. Standard economics accepts a natural science model of economics, assuming that the object under investigation is unchanging just as in the natural sciences the laws of nature are unchanging. ABM economics, on the other hand, assumes a social science model, according to which economics is an object of investigation that gradually changes together with the evolution of the world it investigates.

13As is well known, the proposal of a natural science model of economics is dominant in the field (Davis, 2017). Defenders of this position often point to the law of demand or the principle of comparative advantage as evidence that the principles or laws in economics are unchangeable. On the other hand, supporters of the social science model of economics often point to Myrdal’s concept of circular cumulative causation.

14Among Kirman's (2011) main ideas, is his dissatisfaction with homo economicus regarding the precise identity of an economic agent. Kirman and Teschl (2004) have tried to clarify the rational agent's identity, as he experiences, engages, and interacts with others. Influences of groups to which the agents belong and their impact on those groups are at the heart of problems generated in analyzing the evolution of an economic system. According to Kirman (2010), the structure of interaction between people matters to economics, because in his view the idea of an anonymous market in which people interact through the price system is totally unrealistic.

15Having this perspective in mind, one of this paper’s main claims is that the understanding of the individual as an economic agent remains central to the study of economics, especially in terms of complexity theory and the ABM method. Our epistemological argument is that ABM method should be understood as an innovation in economic methodology, for analyzing human interactions. This methodological innovation requires a more comprehensive concept of the “individual.”

16In our view, it is important to leave behind the concept of traditional rational agent in order to take into account the fact that agents learn from their own experiences of institutional changes, the economic environment, and the behavior of other individuals. Therefore, we argue that these three different epistemological approaches illumine the discussion of the micro-macro relationships of a “complex agent.” In what follows, each of these three epistemological ideas will be applied to the concept of the ABMs’ complex agents. Section 1 presents Popper’s Situational Analysis (SA); Section 2, Simon’s Bounded Rationality (BR), Section 3 Myrdal’s Cumulative Circular Causation (CCC). In Section 4 we synthesize the three concepts of Popper’s SA, Simon’s BR and Myrdal’s CCC in accordance with our paper’s proposal. As final remarks, we sum up our main arguments.

1. Popper’s Situational Analysis (SA)

17Karl Popper investigated the epistemological role of rationality postulate in several different moments of his academic life. Popper (1974) recognizes that both the rationality postulate and situational logic are essential to the development of his analysis of the social sciences. Nevertheless, these concepts did not attract much attention from both professional and most notably academic economists. This is an odd situation, since Popper points out that situational analysis (SA) is a generalization of the method used in neoclassical economics. In part, this can be explained by the fact that Popper’s writings on social sciences methodology were overshadowed by the discussion of falsificationism, rather than verificationism. As Matzner (1997) correctly points out, “In spite of Popper’s forceful plea for ‘situational analysis,’ its impact, compared to the attraction of his ‘falsification criterion,’ was very modest. There are hardly more than a dozen articles in the specialist literature.” (Matzner, 1997; Notturno, 1998, 401).

18Popper (1992a) seeks to construct a model for a trial and error process for searching tentative solutions for a problem situation. Scientific method, Popper argues, follows the scheme: i) the problem in a problematic situation; ii) the existing theories and tentative solutions for the problem; iii) critical discussion; and iv) new problems. The sole purpose of critical discussion (step iii) is to find and eliminate mistakes. Its main concern is not to establish or justify theories, or even to determine a high probability for them. The Popperian approach compares the merits and demerits of two or more theories with a view to establishing their explanatory power (Popper, 1994, 161-162). By comparing theories, we find the one that approximates a solution to the problem (in terms of searching for the unknown truth) and may be considered the best available. Observation, experiment, and measurement, Popper (1994) emphasizes, can only help us in the discovery of our mistakes.

19If a scientist is interested in explaining or predicting a singular event, e.g. the problem of hunger in community C, for example, she will study the universal law, the initial conditions involved, and any other considerations for this specific event. However, if she wants to explain or predict a certain type of event, such as the problem of hunger in any place other than C, she will use a model that represents those typical initial conditions. Popper recognizes that this is done within limits: “We never have sufficient laws and initial conditions at our disposal” (Popper, 1994, 168). After establishing typical initial conditions, Popper (1994, 164) argues, the scientist needs one universal law—the “animating” law—which represents “the way in which the various elements of the model may act upon each other.”

  • 6 Social institutions are understood in a wide sense, such as family, marriage, laws, government agen (...)

20Popper (1979) prefers situational analysis (SA) to situational logic (SL); the latter may lead to a deterministic theory of human action. SL models brings together the typical initial conditions and a universal animating law to analyze human actions and social situations, yet it is a mechanical model and the animating principle is purely abstract. According to Popper, it is “a rudimentary working mechanism” (Popper, 1979, 178). By contrast, SA considers physical things, as well as certain aims and knowledge of or information about social institutions that are relevant to the situation.6

21The method of SA, Popper (1992b) emphasizes, was developed from what he previously called the “zero method” (Popper, 1945, section 29). The main point was to generalize the method of economic theory (marginal utility theory) and make it applicable to other theoretical social sciences. Popper developed a model for social situations, including the institutional situation in which a person is embedded, and how this explains the rationality of her action. These models “are the testable hypotheses of the social sciences; and those models that are ‘singular,’ more specially, are the (in principle testable) singular hypotheses of history” (Popper, 1992b, 118).

22By doing this, Popper considers the social situation, rejecting the reduction to motives and general laws of human nature. The situation matters, as he states that “Our actions are to a very large extension explicable in terms of the situation in which they occur” (Popper, 1966, 97). He does not neglect the role of psychological aspects, but this role is trivial when compared with a detailed description of a person’s action by what he called the “logic of the situation.” It is also extremely difficult and quite impossible to include all psychological aspects in the description of situation. Popper states:

On the contrary: when we speak of ‘rational behavior’ or of ‘irrational behavior’ then we mean behavior which is, or which is not, in accordance with the logic of situation. In fact, the psychological analysis of an action in terms of its (rational or irrational) motives presupposes—as has been pointed out by Max Weber—that we have previously developed some standard of what is to be considered as rational in the situation in question. (Popper, 1966, 97)

The logical investigation of the methods of economics yields a result which can be applied to all social sciences. This result shows that there is a purely objective method in the social sciences, which may well be called the method of objective, understanding, or situational logic. (Popper, 1992a, 79, italics in the original)

23The SA is a conjectural explanation of the human action that appeals to the situation in which the person finds herself (Popper, 1979, 179). This method may be described as an application of the rationality principle as an animating law. “The various persons or agents involved act adequately, or appropriately—that is to say, in accordance with the situation” (Popper, 1994, 169). What is critical is the characterization (a proper description) of the objective situation in which the person finds herself. The rationality principle is a result of analytical models—a by-product from a methodological postulate. The models are empirical explanatory theories (or hypotheses) that are discussed, criticized and empirically evaluated. The rationality principle, Popper (1994, 171-172) emphasizes, is not an empirical explanatory theory; it is only an element (as an approximation to reality) of the general method of SA. There are personal differences not only in knowledge or skill needed to deal with a problem which are part of situation but also in assessing or understanding the situation. For this reason, Popper argues, some people will act appropriately and others not. Popper insists that the “rationality principle is not universally true as a description of our ways of acting” (Popper, 1994, 183).

  • 7 Popper (1994, note 1, 181) explains that he uses the “logic of choice” from Hayek and the “logic of (...)
  • 8 “I may be wrong and you may be right, and by an effort we may get nearer to the truth” (Popper, 196 (...)

24Caldwell (1998) discusses the SA in economics and emphasizes two problems: first, an inconsistency between the methods used by natural and social sciences, since the rationality principle of SA is immune to falsification (see also Hands, 1985, 1992); second, the very nature of the rationality principle, which according to Caldwell (1991 and 1998), is inappropriately vague. This addresses the status of a “rationality principle” for SA. Despite Popper’s claims that he brought the idea of situational analysis and the principle of rationality from economics (Popper, 1994, 154 and 181), this animating principle is only a by-product of his analysis.7 This by-product differs from rationality in the sense of critical attitude, in that it is more a model which delimits “rationality” rather than an analysis of individual rationality that embraces the model. Popper’s rationality means a critical attitude in the presence of problems and their tentative solutions. Popper’s philosophy of science, thus, is confused with a moral rule: to criticize problems and its solutions.8 However, it defends objectivity, which in the case of social science, can be obtained with situational analysis.

  • 9 Related to this issue, another classic problem in the literature refers to the criticism that the r (...)

25For traditional economists, rationality means choosing a course of action in accordance with a complete and transitive preference ordering, and assumes perfect information. In economic jargon, we say that rationality means ‘maximizing expected utility’: the utility of an outcome multiplied by the probability of its occurrence. Furthermore, among all social sciences and humanities, economics is the only one that selects the rationality postulate in order to demarcate its object of investigation. Nevertheless, this is not a consensus position. Use of the rationality principle in economics has been suffering severe attacks, from many different fronts. The most frequent and important criticism refers to the fact that the model of economic rationality would be empirically inappropriate, since its idealized assumptions do not represent properly the true behavior of the real agents.9 Many economists have pointed out that real psychological actors think in ways that are not in accordance to the pure theory of economic rationality (Anderson, 2000; Sen, 1974; Simon, 1969).

26Some philosophers and experimental economists have undertaken to study the characteristics of economic rationality in real human beings through experiments. For example, Axelrod (1984) has used experimental tests to examine how real human beings deal with prisoners’ dilemmas. He found that experimental subjects frequently cooperate rather than defect, a result which is very contrary to the prediction of two-persons game theory. These experimental studies suggest that real persons, and not some abstract idealized agents, behave intelligently, but in ways different from those that would be logical results of axioms of the theory of pure economic rationality. Moreover, since the 1980s, another series of studies has pointed out that real persons do not act ‘rationally’ in many different circumstances. What is meant by the irrationality of an agent are those behaviors not consistent with the constraints imposed by the postulate of rationality.

27Since the assumption of rational behavior has a central importance in economics, it is a major issue for the philosophy of economics. The issue is the empirical adequacy of the concept of rational decision maker, i.e., the assumption that each agent chooses the course of action more favorable to utility maximization. If the actual behavior of the agent does not correspond to these descriptions, and empirical evidence does not support the theory based on rational agents’ action, as critics claim, then this concept should be abandoned.

  • 10 For a discussion about the “rationality principle” used by economics, see Lagueux (1997), who point (...)

28Popper admits that economics inspired his proposal for social sciences, because of its objectivity and the rationality formulation as an “animating principle” in this science. However, this requires a discussion of the status of rationality principle, which is taken for granted in different economic theories.10 SA is derived from economics, principally from the theory of marginal utility; although it is a kind of meta-theory which includes individual choice theory. Preferences, technologies, and constraints (prices, income, etc.) within situational analysis show a person’s situation and her motivation (utility maximization). This situation is analyzed through deduction of a behavior (to buy more or less) that can be expressed in mathematical form. The rationality principle is fixed, insisting that individuals do act appropriately, given the situation, while assuming certain idealized social situations such as a perfect market, monopoly, and duopoly to sustain that principle.

  • 11 For Latsis (1972), the neoclassical program of “situational determinism” in economics demonstrated (...)

29Popper (1979, 169) emphasizes that i) a person with aims and knowledge is put in some abstract and typical situation, and that ii) in order to animate this model, it is assumed that she acts appropriately in the situation in which she finds herself. This is only an animating principle “which is clearly an ‘almost empty’ principle.” In Popper’s perspective it is not possible to argue the rationality of the economic individual without characterizing SA. A constrained analysis of an individual’s rationality may consider only the psychological aspects involved, and for this reason economic models demand the psychological profile of homo economicus. The problem is to consider the psychological aspect as the authoritarian and reductionist principle of the analysis (for example, to maximize profit).11

30Popper’s emphasis on critical rationalism reflects an understanding that is between a methodological principle and a definition of human rationality. Popper’s rationality principle focuses on one determined situation as a model and not one individual action. The rationality principle is not a conception of individuals’ rationality. Popper emphasizes rationality in criticisms (critical rationality), not any principle in human rationality. The methodological individualism principle guarantees only that it is the individual who acts, and not some whole defined for situational analysis. The difference lies in how the scientist understands the situation (complex or not complex) in which individuals are acting.

31With Popper´s SA discussion in mind, we return to the question: is the individual of the ABM model complex in its human nature or may his/her complexity be understood only as a random result of dynamic and uncertain scenarios? Gallegati and Kirman (2012) point out that the agents in the agent-based models “look forward,” are dynamic, learn from their experiences, and react to institutional changes and the behavior of other individuals. The rationality is not given a priori, rather it is the result of dynamic and uncertain social constructs. In what follows we argue that Simon provides a rationality concept more suitable to social constructs.

2. Simon’s Bounded Rationality (BR)

32According to Beinhocker (2006) the traditional rational agent assumption is criticized, but nevertheless used, because that enabled the models to be mathematically tractable. Herbert Simon and his colleagues, in the 1950s, provided a more direct challenge: they watched real people making decisions and presented the bounded rationality concept as an alternative to traditional rationality approach. They pointed out our lack of perfect information and confirmed the large but still finite processing power of our brains. We satisfice, according to Simon, by taking the information we have as it comes, and we do the best we can with it. After Simon, two generations of economists and psychologists began to build empirical and experimental evidence against the traditional model of Homo Economicus. Kahneman and Tversky, in the 1970s, published a series of papers on how real people diverge from the basic assumption of traditional economics. In the 1980s and 1990s, researchers following these insights and proposals created the behavioral economics, that study how real behavior deviates from the traditional theoretical one.

  • 12 The year of first edition is originally 1947, this is: a very early treatment of rationality in eco (...)

33Herbert Simon brought to economics (and to other sciences that deal with decision or choice theory) an important criticism about of the traditional view of rationality in an attempt to make rationality in economics a more realistic theory. In his seminal work about administrative behavior (Simon, 1965), he departed from rationality in the traditional exposition as a theoretical relation of means and ends.12 Simon criticizes traditional treatments of rationality as a proper adequacy between means and ends in a serial and well defined hierarchical form, as he stated that: “Both organizations and individuals … fail to attain a complete integration of their behavior through consideration of these means-end relationships,” so “what remains of rationality in their behavior is precisely the incomplete, and sometimes inconsistent, hierarchy of that has just been described” (Simon, 1965, 64).

  • 13 This occurs, according to Simon, in two fundamental aspects: i) when an end is some state or condit (...)
  • 14 Knowledge is identified by Simon as a primary influence on choice. Preferences, which have a centra (...)

34Simon listed three limitations of this means-end hierarchy: i) ends attained by the choice of an alternative are often incompletely and incorrectly stated (as a failure to consider all alternative ends); ii) the impossibility of a complete separation of means from ends in terms of the neutrality of alternative means (alternative means may have unsought results/ends and many consequences which, theoretically, must be properly weighted in advance); iii) this means-end approach tends “to obscure the role of the time element in decision-making”13 (Simon, 1965, 65). In this work, Simon proposes that choices can be better understood in terms of alternative and consequences (more specifically: alternative behavior, linked with subjective designing of strategy), the need to consider knowledge (as a tool to determine a whole class of possible consequences correlated with each of the alternative strategies),14 as well as the influences of group behavior over individual decision (in the sense that cooperation or competition is an issue). In this way, decision-making relates values and possibilities. All these elements are, in general, the same concerned with by choice theory in economics, nevertheless Simon’s approach is not as a defense of axiomatic affirmations about these properties and relations, but of their empirical adequacy to explain and understand human choice as rational behavior.

35Hence, according to Simon (1965, 75), “rationality is concerned with the selection of preferred behavior alternatives in terms of some system of values whereby the consequence of behavior can be evaluated.” But may rationality, asks Simon, be considered only in conscious way, or may unconscious processes also be considered as part of rationality? In an attempt to address this point, he seeks to clarify the problem of rationality by applying four qualifiers:

Perhaps the only way to avoid, or clarify, these complexities is to use the term “rational” in conjunction with appropriate adverbs. Then a decision may be called “objectively” rational if in fact it is the correct behavior to maximizing given values in a given situation. It is “subjectively” rational if it maximizes attainment relative to the actual knowledge of the subject. It is “consciously” rational to the degree that the adjustment of means to ends is a conscious process. It is “deliberately” rational to the degree that the adjustment of means to ends has been deliberately brought about (Simon, 1965, 76).

36Simon breaks with a consensus in sciences in which rational decision (or choice) plays a central role. In the 1950s, there was a more or less widespread conviction that it would be possible to represent all rational forms of behavior as problems of constrained optimization. However, as rational decision-making models turned to increasingly complex situations, there was a corresponding increase in the complexity of the calculations and in the refinement of the algorithms needed to solve them. This raised the question: are individuals capable of executing such decision-making processes, as economic theories presumed.

37Simon criticized this kind of theoretical propositions for its lack of empirical content. Early in 1947, Simon advanced his critique of the limits of rationality on both theoretical and empirical grounds. In his view, objective rationality implies:

that the behaving subject molds all his behavior into an integrated pattern by (a) viewing the behavior alternatives prior to decision in panoramic fashion, (b) considering the whole complex of consequences that would follow on each choice, and (c) with the system of values as criterion on singling out one from the whole set of alternatives. (Simon, 1965, 80)

38Conversely, he states that “Real behavior, even that which is ordinarily thought of as ‘rational’ possesses many elements of disconnectedness not present in this idealized picture” (Simon, 1965, 80). He adds that “behavior reveals ‘segments’ of rationality—that behavior shows rational organization within each segment, but the segments themselves have no very strong interconnections” (ibid., 81). Objective rationality “falls short” in three ways, according to Simon (1965, 81): i) the requirement of complete knowledge in anticipation of the consequences on each choice—“knowledge of consequences is always fragmentary;” ii) consequences lie in the future, so imagination must complete the lack of experienced feeling capable to attach value to them—“values can be only imperfectly anticipated;” iii) the requirement of contingent choice among all possible alternative behavior—instead, “only a few of all these possible alternatives ever come to mind.”

  • 15 Simon borrows these limits to human intellect from Psychology, in the statement that to this scienc (...)

39Simon (1955; 1957; 1978) enriched his hypothesis of bounded rationality by observing that among reasons for imperfections in human decision-making is that reasoning is a resource-consuming activity, i.e. an activity which also involves costs for the agent. These costs arise from the existence of various limitations: environmental, psychological, and/or cognitive. Such limitations are unavoidable for the human intellect.15

  • 16 About this definition of bounded rationality, in simplified terms, writing to another (in non-econo (...)

40The domains of bounded rationality involve real situations in which agents are constrained by one or more of the following: they do not have complete information, do not have the enough time, and do not have the necessary cognitive means for the absolutely rigorous and definitive calculation of which option is best among different alternative courses of action. Therefore, even those individuals seeking to make rational decisions would be incapable of doing so and, consequently, would be obliged to make suboptimal choices in complex situations (Simon, 1957; 1985; 1986).16

41Simon’s (1957) model of bounded rationality proposes that cognitive limitations lead decision-makers to construct more simplified models for dealing with the world. Simon (1957, 198) argued that the decision-maker’s behavior is not nearly optimal in relation to the real world. To predict his/her behavior, we must understand the construction of this simplified model and its relation to such psychological issues as perception, thinking, and animal learning.

  • 17 In his more formal work on this (Simon, 1955, 102-103), Simon presents the three “classical” (in hi (...)

42Simon developed a cognitive strategy which substitutes for the widely held concept of optimization:17 the “satisficing” principle. This principle enabled him to explain the behavior of agents looking for a “good enough” option in an uncertain environment where the search for alternatives is costly, the knowledge is limited and fragmentary, and time influences the contingent choices. Satisficing is a heuristic that involves choosing the first alternative that meets your minimum requirements. This approach, simple in terms of cognitive operators, requires less of scarce mental resources. However, it may lead to suboptimal behavior since, upon finding an acceptable option, the search for and evaluation of possibly better alternatives ceases.

  • 18 For a criticism of rationality in economics in an Institutionalist perspective, see Hodgson (2012).

43In terms of ABM methods, Simon’s bounded rationality is a framework of analysis with more realistic assumptions and may be empirically evaluated. Thus, the basis for Simon’s principal criticisms of neoclassical economics' substantive rationality approach, is that it is “an exceedingly weak theory, as shown by the difficulty of finding sets of facts, actual or hypothetical, that cannot be rationalized and made consistent with it” (Simon, 1986, 223). Yet, instead of admitting those failures, neoclassical economists “are prepared to make whatever auxiliary empirical assumptions are necessary in order to preserve the utility maximization postulate, even when the empirical assumptions are unverified” (Ibid., 222).18

  • 19 For a revision of this literature, see Rabin (2013).
  • 20 Newcomb’s paradox was first presented in Nozick (1969). Here, we use also the analysis of this para (...)

44Simon’s approach to rationality theory has been applied in empirical exercises to real world and laboratory controlled conditions. This approach is well suited to the broad view of experimental economics, game theory, and ABM methods.19 The following example is similar to tests conducted in experimental economics. It illustrates that neoclassical economics rationality theory may lead to incorrect predictions about people's reasoning and choice. It’s the Newcomb’s paradox.20

45The problem can be stated as follows: one agent is presented two boxes. One of them is transparent, and the agent can see that it contains $1000 inside. The other one is opaque. The agent can’t see what is inside, but is told that it may contain either a $1,000,000 or nothing ($0) at all. This agent is allowed only one of two strategies:

S1: to take what is in the opaque box, alone;

S2: to take what is in both boxes.

46At the moment when the agent is being presented the boxes and his/her options, an omniscient being who can predict the agent’s choices with certainty makes a contingent decision: this omniscient being will put one million dollars inside the opaque box if and only if it predicts that the agent will choose S1. The dynamics are as follows: the omniscient being makes its prediction and then puts the $1,000,000 in the opaque box, or does not, depending upon its prediction; then, the agent is allowed to make his/her choice.

  • 21 It is not the aim of this work to try to give a complete and definitive answer to a problem still o (...)
  • 22 By risking the possibility to take nothing, they can be rewarded earning the maximum payoff of the (...)

47In rational terms, S2 is a dominant strategy in this problem. This strategy applies the sure thing principle, which can be read with Simon (1995) as the certainty rule. By another perspective, a fully rational agent must choose S2, the strategy which is consistent with Max-min rule. This maximizes his/her payoffs in the worst-case scenario by taking $1000 instead of nothing at all. But in such experiments (as related by Dupuy, 2014), three of four experimental subjects choose S1, in a clear violation of what rationality theory would predict as a dominant strategy. Strategy S2 is chosen most frequently by professionals in studies in choice theory (as Dupuy specifies: professional philosophers, game theorists, and other experts in this field). Ordinary people, in experiments, deliberately refuse the dominant strategy. Is it an irrational decision?21 We suggest that irrationality as an answer to this apparent inconsistent choice is not a good explanation. Individuals who violate substantive rationality predictions by choosing strategy S1 are acting in a satisficing way, with the limited knowledge that they possess.22

3. Myrdal’s Cumulative Circular Causation (CCC)

48Swedish economist Gunnar Myrdal’s model called “Cumulative Circular Causation” (CCC) attempts to account for the persistence of spatial social-economic differences among nations and regions within nations. CCC is the key concept of his institutional economics. Unlike classical and neoclassical economists, Myrdal does not advocate that an economy shows any gravitational tendency to equilibrium, because social systems and economic processes do not develop towards a stable situation. He holds that a change does not create an opposite reaction, but other changes that emphasize it. In fact, factors tend to show cumulative effects, either to positive or negative cycles. As Myrdal (1957, 13) states:

The position of balancing forces which thus becomes established is, however, not a natural outcome of the play of the forces within the system. The position is, furthermore, unstable. Any new exogenous change will by the reactions in the system again start a cumulative process away from this position in the direction of the new change...the very opposite of a natural tendency towards equilibrium, endogenous to the system.

49Myrdal’s circular cumulative causation is a counterpoint to the monocausal linear causality approach used by neoclassical economics. Myrdal defined two distinct elements of the circular causation (namely, the circular causation itself and its cumulative effect) in his book Asian Drama—An Inquiry into the Poverty of Nations (1968), where he declares:

circular causation will give rise to a cumulative movement only when … a change in one of the conditions will ultimately be followed by a feedback of secondary impulses … big enough not only to sustain the primary change, but to push it further. Mere mutual causation is not enough to create this process. (Myrdal, 1968)

50According to his view, international trade between industrialized and developing countries, for instance, could increase differences between them because of the spread effects in the more developed/industrialized areas and negative effects in backward/nonindustrialized/traditional areas (countries). The direction of the processes depends on the initial situation to be explained and the factors causing the observed changes.

  • 23 Backwash effects are divergent processes that retard growth (or reinforce poverty) in certain areas (...)

51His development theory states that economic (regional or global) inequalities between rich and poor (regions or countries) are growing due to the unbalanced economic growth. The cumulative process can occur in either direction, positive or negative, and if unregulated, the negative effect tends to increase disparities between regions. Indeed, he identified two types of effects, named “backwash” (unfavorable, negative) and “spread” (favorable, positive) effects.23

52Myrdal’s original formulation of the CCC concept came to light for the first time in Appendix 3 of American Dilemma—The Negro Problem and Modern Democracy (1944). At that time, he used this concept as a research hypothesis for the circular (self-reinforcing) causation among prejudices, institutions, and poverty. This self-reinforcing causation triggered a vicious cycle of cumulative effects of increasing inequalities and poverty. On the other hand, spread effects are convergent processes where new growth stimuli might induce a self-reinforcing movement into a higher level of development.

53Myrdal uses the notion of a vicious (or virtuous) circle to explain how a process becomes circular and cumulative, where a negative (or positive) factor is, at the same time, cause and effect of other negative (or positive) factors: “The concept implies, of course, a circular constellation of forces tending to act and react upon one another in such a way as to keep a poor country in a state of poverty” (Myrdal, 1957, 11). Figures 2 and 3 illustrate both positive and negative circular cumulative effects of two hypothetical economies.

Figure 2: Circular Cumulative Causation: Positive Effects in Flourishing Region

Source: Author’s figure, based on Myrdal (1957).

Figure 3: Circular Cumulative Causation: Negative (Backwash) Effects in Poor Regions

Source: Author’s figure, based on Myrdal (1957).

54In the context of Agent Based Modeling research, the concept of circular cumulative causation is to be understood in terms of interactions between the effects that science is assumed to have on the world and the effects the world is assumed to have on science. This is a two-way causal relationship which implies that the content of economics and the world gradually change together (Davis, 2017).

55According to Gallegati and Kirman (2012, 15), the ABM method is characterized by two main tenets: it presupposes the existence of a multitude of objects (“agents,” also called “individuals”) that interact not only with each other, but also with their environment. Besides, the objects are heterogeneous and autonomous, in the sense that there is no “top down” control over their behavior. It is also worth highlighting that “agents are allowed to have local interaction and to change their individual rules (through adaptation) as well as the network which drives their interactions.” While interacting, emergent properties and behavior begin to arise at the individual level (circular causation), establishing a macro foundation for micro behavior. That means: the agents learn from their own experiences and react to institutional changes and to other individuals’ behavior. Rationality is not given a priori, rather is the result of dynamic and uncertain social constructs. Summing up, according to the ABM, the underlying assumptions on about individual behavior can be weakened in comparison to the assumptions of utility maximization adopted by traditional economics. In this sense, from the epistemological perspective, the ABM approach and its emphasis on the complex theory view are in direct opposition to the axiomatic approach of neoclassical economics.

4. Poppers SA, Simon’s BR and Myrdals CCC: a Way Out?

56It is possible to synthesize the three concepts of Popper´s SA, Simon´s BR and Myrdal´s CCC in accordance with our paper proposal that involves these questions: i) to what extent must individuals in ABM be necessarily treated as complex? ii) what relevance has the concept of an individual in ABM, and to what extent is this different from mainstream economics? and iii) does ABM offer a different approach to evaluating the models as a whole, but, more importantly, the individuals?

57It is possible to draw a link between the logic of ABM, especially in that rationality is not given a priori, but is the result of dynamic and uncertain social constructs and Popper’s SA as applicable to social sciences. To Popper, rationality of the individual means only that the individual acts according to each specific situation, with no presumption of behavior, that is, the individual rationality is the result of the model and not an assumption, like homo economicus. In terms of ABMs, heterogenous individuals follow rules of action in accordance with each specific situation, what is to say: the individual is not complex in his nature. The individual behavior can be understood as a random result of dynamic and uncertain scenarios. This is important to consider specifically in ABM computational modelling.

58Popper argues that his rationality principle is not an a priori definition for human behavior as it is for the rational individual in traditional economics. Also, he mentions that individuals could act rationally or not, but it is important to define the situation in which the individual will act. This principle is not empirical and is not falsifiable, but the situational analysis model is important and is falsifiable.

59For Epstein (1999, 48) ABM and behavioral research are complementary. He mentions that the diverse laboratory and experimental work on decision-making is giving an ever-clearer picture of how homo sapiens—as against homo economics—makes decisions. Epstein states that a great lesson of agent-based models is that even perfect knowledge of individual decision rules does not always allow us to predict macroscopic structure. We get macro-surprises despite complete micro-knowledge. It is possible to study the micro-to-macro mapping with ABM, and it is essential to begin with solid foundations regarding human behavior. Behavioral research is getting closer to these issues. But Epstein also argues that we will still need techniques for projecting the macro level from there (particularly for spatially-distributed systems of heterogenous individuals). Agent modeling offers behavioral social science a powerful way to do that.

60It is possible to think of ABM like an SA with a boundedly rational agent in the sense that rationality is a result of the model, and not the contrary. Again, note the importance of the model and its assumptions. For Epstein (2008) the question is not whether to build models, rather it is to build them with explicit assumptions laid out in detail so that it is possible to study what they entail. A researcher can in fact calibrate to historical cases if there are data, and can test against current data to the extent that it exists. Without models, in other words, it is not always clear what data to collect (Epstein, 2008, 3). For Epstein (2008, 4) all models are idealizations and the issue is whether the model offers a fertile idealization. More importantly, Epstein (2008) emphasizes that the importance of the modeling enterprise is that it enforces a scientific habit of mind, one of militant ignorance—an iron commitment to “I don't know.” All scientific knowledge is uncertain, contingent, subject to revision, and falsifiable in principle (Epstein, 2008, 4). Popper’s critical rationalism seems to be very compatible in this regard on this point.

61According to Grabner (2016), the basic idea of ABM is to specify the fundamental entities (especially the economic agents and their relations) in an adequate manner, and to study the systemic and dynamic consequences of this configuration. Therefore, it allows heterogeneous and boundedly rational agents in Simon’s sense as we showed above, but directly interdependent and socially embedded in their environment—just like Myrdal’s CCC approach. When employed on agents, they can help to simulate the learning behavior of agents and their way of adapting to their environmental requirements. This is one source for the ability of ABMs to resemble the principle of (circular) cumulative causation of real-world dynamics, as we have argued above.

Final Remarks

62According to the alternative view we proposed here, Myrdal’s circular cumulative causation process is the antithesis to the linear causality and mechanistic analogy adopted by neoclassical economics. Since over historical time an event can be both cause and effect of other cumulative forces, that gives rise to the possibility of virtuous and vicious cycles within economy. This is a more realistic approach to how agents with bounded rationality interact with each other and with their environment.

63Popper’s Situational Agent and the rationality principle taken together make it possible to argue that the individual of the ABM model is not the same perfectly rational individual of traditional economics. He/she resembles Popper’s individual once his/her actions are in accord with more complex scenarios. Such complex scenarios could include not only institutions but also personal differences. Such personal differences involve not only the knowledge and skills needed to deal with a situational problem but also to understand it. For this reason, Popper argues that some people will act appropriately and others will not because the rationality principle is not universally true as a description of an agent’s choices.

64One may argue that Popper´s Situational Agent and his defense of the rationality principle as an animating law and not as an a priori fixed rationality principle like the homo economicus resembles Simon´s bounded rationality and adaptive complex system. This model of human behavior is radically opposed to the neoclassical view. The economy, governed by what Simon called bounded rationality, concerns real contexts, real agents, and the existence of many constraints, including incomplete information, lack of time, and/or a lack of cognitive means for maximizing expected utility.

65Computational treatment of these insights is a challenge, which discussion is beyond the scope of present work. Our main concern here is to present an epistemology of rationality and of individual behavior as insights that could guide ABM modelling in future developments. Economic theory can be enriched by agent-based modelling with its more realistic characterization of the humanity of individuals and their behavior living in a dynamic environment. Economic theory need not be guided by the simplistic, idealized rules of a maximizing approach that reduces individuals to fully rational decision machines. Instead, agent-based modeling views individuals as people, realistically portrayed, able to learn, with virtues and faults, complexities, limitations, purposes, and vision, as human beings truly are.

The authors thank the participants of the Workshop “From thought experiments to Agent Based Models and calibration: Reflecting on the many facets of simulations in economics” that took place on October 2019 at Maison des Sciences Economiques (Université Paris 1 Panthéon-Sorbonne), where a first version of this paper was presented, and two anonymous referees for their helpful comments. They are also indebted to Judy Kash and Robin Kash, for their precious comments and final English revision and assistance. The usual disclaimer applies.

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Notes

1 We use the terms “epistemology” and “epistemological analysis” in its more traditional meaning, i.e. the one related to the theory of knowledge, especially with regard to its methods, validity, and scope, and to the distinction between justified belief and opinion.

2 Some contributions to this discussion are Holland (1975); Holland and Miller (1991); Bowles and Gintis (2000); Davis (2007) and Kirman (2011).

3 The “El Farol bar problem” is a problem in game theory modelled as a static game, as follows: every Thursday night a group of people want to go to the El Farol Bar. However, the place is quite small, and it's no fun to go there if it's too crowded. The preferences of the population can be described in the following terms: i) If less than 60% of the group go to the bar, they'll all have a better time than if they stayed at home; ii) If more than 60% of the group go to the bar, they'll all have a worse time than if they stayed at home. As it is a static game, it is necessary for everyone to decide at the same time whether they will go to the bar or not.

4 Pyka and Fagiolo (2005), for instance, states that besides the various labels under which different classes of ABMs have become known among economist scholars, they share a common set of qualitative assumptions that reflect their underlying modelling philosophy.

5 The term “Methodology” is used here as well in the hole text in the philosophical sense of “an epistemological analysis of economic method” and not in the more pragmatic sense of a “toolbox.”

6 Social institutions are understood in a wide sense, such as family, marriage, laws, government agencies, etc. This definition also includes physical institutions, such as roads, sanitation, electricity provision grid, or what is generally understood as infrastructure.

7 Popper (1994, note 1, 181) explains that he uses the “logic of choice” from Hayek and the “logic of historical problem situations” to compose his “logic of the situation.” The “logic of situational choices” does not see choice in the deterministic form. See also Popper (1979, 178), quoted in section 1, about the use of the name “situational logic.”

8 “I may be wrong and you may be right, and by an effort we may get nearer to the truth” (Popper, 1966, 238). This is a rule that can be applied in both practical and scientific fields.

9 Related to this issue, another classic problem in the literature refers to the criticism that the rationality principle would promote a—unwanted—confusion between the positive and the normative domains in standard economic theory. See, for example, Frank, Gilovich, and Regan (1993). Despite the importance of this issue, since it does not refer to the scope of the article, its treatment is not addressed here.

10 For a discussion about the “rationality principle” used by economics, see Lagueux (1997), who points out, through a historical analysis of economic thought, when this principle started to play a fundamental role in economics. Alternatively, for an exposition about Popper and the rationality principle as an animating principle, see Lagueux (2002).

11 For Latsis (1972), the neoclassical program of “situational determinism” in economics demonstrated that rationality principle was trivial (almost empty), because human behavior (profit maximization, or other) is rather institutionalized in the complex interactions (social, physical, and psychological), under perfectly competitive conditions. The situation is different with the “emergence of economic behaviorism,” when was detached the importance of the nature of decision-making agents under imperfect conditions (risk, uncertainty, ignorance).

12 The year of first edition is originally 1947, this is: a very early treatment of rationality in economics which is very insightful, but was neglected in most of microeconomic theory born in the 1960’s with reformulation in choice theory and general equilibrium approach made by Arrow-Debreu (Arrow and Debreu, 1954).

13 This occurs, according to Simon, in two fundamental aspects: i) when an end is some state or condition to be attained in an specific time, there is only one state (one result) at one time, but this is not unique—there could be other ends in different (sequential) times, and different ends in different times can influence choice from now; ii) decisions taken in time can be irrevocable as it creates new situations which influences the following decisions after it.

14 Knowledge is identified by Simon as a primary influence on choice. Preferences, which have a central point in economic choice theory and rational behavior of economic agents, are influential in secondary order. Neoclassical economics, otherwise, admits theoretically perfect knowledge of economic agents as an axiomatic statement. Simon’s theory of bounded rationality departs from this axiomatic schema, as his theory try to cope with the psychological treatments of human behavior, and perfect knowledge is not an empirical observation in real world agents, as Psychology understands this point. Simon states: “Everyone agrees that people have reasons for what they do. They have motivations, and they use reason (well or badly) to respond to these motivations and reach their goals. Even much, or most, of the behavior that is called abnormal involves the exercise of thought and reason.” (Simon, 1986, 210). And then: “I emphasize this point of agreement…—that people have reasons for what they do—because it appears that economics sometimes feels called on to defend the thesis that human beings are rational. Psychology has no quarrel at all with this thesis. If there are differences in viewpoint, they must lie in conceptions of what constitutes rationality, not in the fact of rationality itself.” (Ibid., 211). Economics has been a science building in which substantive rationality, based in perfect knowledge and preference relations in axiomatic basis is the cornerstone. Psychology is not concerned with this limitation. Simon advocates an Economic Science in which this non-observational approach of substantive rationality can be replaced by its bounded rationality treatment.

15 Simon borrows these limits to human intellect from Psychology, in the statement that to this science human beings are rational, but have biological limits in treating with objective situations. Simon calls the difference between rationality in Economics and in Psychology a difference between objective and procedural rationality (Simon, 1976; 1982; 1986). As he stated “in economics, rationality is viewed in terms of the choices it produces; in the other social sciences, it is viewed in terms of the processes it employs…The rationality of economics is substantive rationality, while the rationality of psychology is procedural rationality.” (Simon, 1986, 210).

16 About this definition of bounded rationality, in simplified terms, writing to another (in non-economics field) audience, he states: “if we take into account the limitations of knowledge and computing power of the choosing organism, then we may find it incapable of making objectively optimal choices. If, however, it uses methods of choice that are as effective as its decision-making and problem-solving means permit, we may speak of procedural or bounded rationality, that is, behavior that is adaptive within the constraints imposed both by the external situation and by the capacities of the decision maker.” (Simon, 1985, 294).

17 In his more formal work on this (Simon, 1955, 102-103), Simon presents the three “classical” (in his terms) concepts of rationality: a) Max-Min rule—in which agents chose the alternative that maximizes the worst payoff attainable since the worst possible outcome will ensue, whichever be the alternative chosen; b) Probabilistic rule—in which agent maximizes the expected value for a probability distribution (assumed known) of outcomes; c) Certainty rule—in which agent, knowing that to each alternative there is a well specified payoff in a set of future state conditions, choose that behavior alternative whose warranted outcome is the largest.

18 For a criticism of rationality in economics in an Institutionalist perspective, see Hodgson (2012).

19 For a revision of this literature, see Rabin (2013).

20 Newcomb’s paradox was first presented in Nozick (1969). Here, we use also the analysis of this paradox done in Dupuy (2014).

21 It is not the aim of this work to try to give a complete and definitive answer to a problem still open to different views.

22 By risking the possibility to take nothing, they can be rewarded earning the maximum payoff of the trial as well: they can earn nothing at all, indeed, or earn one thousand (in a conservative choice), but they can earn a payoff which is many times greater than the payoff of the rational, dominant, conservative and “predictable” strategy. In this sense, they were bounded in rationality, but used to be rational as they choose the strategy that gives the maximum payoff, in satisficing terms: they prefer the maximum attainable to his choices, or nothing, instead of “something or nothing.” They already have nothing in the start of the game, so they can gain a very huge amount, by choosing S1, or leave with nothing, as they already have from the start. Why to lose the opportunity of a greater outcome, when is possible to risk little (losing $1,000, with certainty) and get it (gaining $1,000,000 if they choose S1)? So, this possibility of a very huge payoff by choosing S1 is viewed as better than choosing S2: is better to risk and gain a greater sum, than, using de sure principle, to get only $1000. The magnitude matters. This is the reason why they choose S1. These are results of the kind of analytical problems which ABM methods can treat, using bounded rationality as theoretical approach.

23 Backwash effects are divergent processes that retard growth (or reinforce poverty) in certain areas or countries due to the lack of external economies. In general, as an example, if an area is very poor, its poverty can create an environment in which poverty feeds itself: lack of opportunities creates behaviour like trend to emigration of young people leaving this area looking for new opportunities elsewhere, elders and children, or less productive workers left behind maintain that area with poor economic dynamics, and so poverty can be a trap: new generations will repeat this cycle. Poverty creates conditions that feeds new cycles of poverty. Spread, in the contrary, is a situation in which benefits of some changes creates new opportunities that generates growth and new opportunities coming continuously.

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Table des illustrations

Crédits Source: Author’s figure, based on Myrdal (1957).
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Crédits Source: Author’s figure, based on Myrdal (1957).
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Solange Regina Marin, Brena Paula M. Fernandez et Daniel de S. Vasconcelos, « Agent Based Models and Complex Individuals: An Epistemological Analysis »Œconomia, 10-2 | 2020, 231-256.

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Solange Regina Marin, Brena Paula M. Fernandez et Daniel de S. Vasconcelos, « Agent Based Models and Complex Individuals: An Epistemological Analysis »Œconomia [En ligne], 10-2 | 2020, mis en ligne le 01 juin 2020, consulté le 22 avril 2021. URL : http://journals.openedition.org/oeconomia/8173 ; DOI : https://doi.org/10.4000/oeconomia.8173

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Auteurs

Solange Regina Marin

Department of Economics and International Affairs, Federal University of Santa Catarina (UFSC-Brazil), solange.marin@ufsc.br

Brena Paula M. Fernandez

Department of Economics and International Affairs, Federal University of Santa Catarina (UFSC-Brazil), brena.fernandez@ufsc.br

Daniel de S. Vasconcelos

Department of Economics and International Affairs, Federal University of Santa Catarina (UFSC-Brazil), daniel.s.vasconcelos@ufsc.br

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