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http://www.gmu.edu/departments/economics/vaughn/COMPLEX.html.

Hayek’s Theory of the Market Order as an Instance of

the Theory of Complex, Adaptive Systems

Karen I. Vaughn

George Mason University

I wish to Peter Boettke and Barkley Rosser for helpful comments on an earlier draft of this paper, and Loren Poulsen for research assistance in the early stages of writing this paper. I also wish to acknowledge the generous support of the Earhart Foundation in the preparation of this work.

Hayek’s Theory of the Market Order as an Instance of

the Theory of Complex, Adaptive Systems

Karen I. Vaughn

George Mason University

In recent years, a new approach to economics has begun to emerge that models economies as evolving complex systems rather than as optimization problems. Although becoming increasingly widespread, this approach, an application of the more general, and also recently developed, science labeled "complexity theory" by its practitioners, is still largely associated with the Sante Fe Institute and with the work of Brian Arthur. In a recent interview about the new science of complexity, Arthur was quoted as saying, "Right after we published our first findings [about the implications of complexity theory for economics], we started getting letters from all over the country saying, ‘You know, all you guys have done is rediscover Austrian economics’.....I admit I wasn't familiar with Hayek and von Mises at the time. But now that I've read them, I can see that this is essentially true." [Tucker,p.38] The purpose of this paper is to explore the degree to which Arthur's claim is, itself, "essentially true," at least with respect to the economics of Friedrich Hayek. Does complexity theory really capture a Hayekian understanding of a market economy?

Austrians might well be skeptical of claiming a linkage between Hayek and complexity theory. Complexity theory is both mathematically sophisticated and to a great degree the product of the development of bigger and faster computers that can generate solutions to large systems of non-linear equations. As such, complexity theory employs techniques of analysis that are totally foreign to traditional Austrian modes of explanation. Further, complexity theory purports to find similarities across a broad spectrum of scientific areas from astronomy to physics to biology and, now, to economics. As a consequence, some, and not just Austrians, have been inclined to dismiss a theoretical construct that appears to claim to explain everything of interest in the world as more hype than science. [See, for example, John Horgan, 1995] Austrian skepticism, additionally, could be exacerbated by the tendency of some complexity theorists like Arthur or, more recently, Paul Krugman, to use complexity theory to reveal more and more instances of potential market failure. However, despite these very real worries, it seems inescapable that Arthur’s statement about "rediscovering" Austrian - or at least Hayekian - economics is in large part correct.

I will argue in this paper not only does the theory of complex, adaptive systems capture the main features of Hayek’s theory of spontaneous market order, in fact it would be surprising if it did not do so. Indeed, Hayek was himself in some sense a pioneer in developing the theory of complex systems in the 1950's when the scientific problems that were precursors to modern complexity theory were being discussed. I will further argue that the theory of complex, adaptive systems may provide a useful analogy to help in explicating the theory of spontaneous market order to the scientifically minded, and in particular, can buttress Hayek’s critique of central planning. Finally, I will argue that Hayek’s insights about spontaneous market orders can themselves help to interpret the results of complexity theory as they are applied to real world conditions.

What is complexity theory?

Complexity theory is the name given to a set of ideas that have emerged in the last three or four decades from several disciplines such as computer science, information theory, evolutionary biology and cognitive psychology. In general, complexity theory deals with non-linear systems with many interdependent variables. Because of the non-linearity of complex systems, the history of the development of complexity theory is closely linked with the development of computer technology. Without computers, most complex systems are impossible to investigate. Computer scientists discovered earlier in this century that they were incapable of programing a computer directly to find the optimum solution to a large system of non-linear equations. Consequently, they began to investigate such systems indirectly by using genetic algorithms, rules of operation that mimic competition among artificial agents who possess alternative strategies for achieving some end. These artificial agents compete for computer time, and those strategies that yield the highest pay-offs come to dominate in the solution set. Even these more indirect methods of solving non-linear systems are highly computationally intensive, and they do not yield clearly defined maxima, but they do give better solutions than any possible alternative. The claim is that such artificial agents operating according to defined rules based on local information mimic many complex systems found in nature such as weather patterns, the movements of astronomical bodies, chemical interactions, biological systems and even some human institutions.

All complex systems, whether cosmological, biological or artificial, display several common properties. As John Holland describes it, all complex systems are networks of many independent "agents" that interact with one another according to some internal set of rules or strategies. At the simplest level in biology, for example, molecules are either attracted or repelled by other molecules in a particular environment, while more complex collections of molecules have a repertoire of strategies to call upon to navigate through their environment and to reproduce themselves. The interaction of these agents gives rise to the development of "emergent properties" that are different from the properties of the individual agents and cannot be explained simply with reference to the properties of the component agents. For example, we may know a great deal about the details of individual water molecules, and we may know that clouds are composed of water vapor. We cannot, however, explain the behavior of clouds by referring solely to the properties of water molecules because the behavior of clouds depends upon the interactions among the molecules.

Emergent properties are said to be the consequence of self-organization because they arise solely from the inherent behavioral strategies of the agents acting on their local knowledge: there is no central controller to "tell" agents to form larger units, nor does any agent have complete knowledge of the circumstances surrounding its actions.

Complex systems often tend to be hierarchical in the sense that each level of emergent properties serves as building blocks for more complex arrangements. Genes organize into chromosomes which form the building blocks of cells which form the building blocks of tissues which organize into organs which organize into bodies which organize into social groups. Each level is composed of elements from the simpler level. Further, the more complex level is only possible because of the prior organization of the simpler level. Obviously, the hierarchical nature of complex adaptive systems implies that the course of development is path dependent: the characteristics of one level depends upon the emergent characteristics of the simpler level.

Most important for our purposes, complex systems also tend to be adaptive systems. That is, the agents in these systems in some sense learn better to deal with their environment. They are continually organizing and reorganizing their building blocks according to the payoffs they receive from their activities, i.e. according to the reproductive success of their new organization. Since the payoffs agents realize depend heavily upon the actions of other agents, they tend both to cooperate with some agents and to compete with others to improve their environmental adaptability. What primarily drives such behavior is the agents’ ability to learn from their environment.

Learning is at the core of the theory of complex, adaptive systems. What the agents learn in a complex system are new strategies of action. If we think of strategies as "predictions" of the consequences of their actions (if I do x, y will follow), revising strategies depends upon some form of feedback from their actions (I did x, but z followed, try doing w instead). Where feedback exists, the system continues to become more and more mutually adapted.

As in genetic evolution, adaptability is really another word for what works in a particular environment - what leads to reproductive success. But since in complex adaptive systems, the environment is composed of other agents all pursuing their own strategies, a highly adapted system is one in which agents adapt to the strategies of each other though competition and cooperation. This continual process of prediction (i.e. choosing an available strategy to fit the circumstances) and feedback (receiving the payoffs of the strategy) leads to greater and greater levels of organization. It also leads to more variation in the system as the adaptive strategies of some agents open up niches for other agents to exploit. Consequently, complex adaptive systems never settle down to a determinate equilibrium. They constantly generate novelty via opportunities to be exploited by other agents in a process that Austrians will find reminiscent of the Kirznerian entrepreneur. [John Holland as summarized in Waldrop:145-147]

Certainly, there are apparent similarities between Hayek's account of a market economy and the major propositions of complexity theory. Complexity theory is about self-organization of individual units into unexpected groupings that contain properties beyond those descriptive of the units alone. Hayek's theory of "spontaneous order" is concerned with explaining social order as an unintended, undesigned outcome of purposeful human actions. Complexity theory is essentially about information; its organization, communication and evolution while Hayek's philosophy of science, his theory of the brain, his understanding of a market economy and his theory of social evolution all revolve around his essential insights about the nature and limitations of human knowledge. Complexity theory is based on non-linear relationships among many variables for which there is no unique solution; Hayek has long argued that economics because of its complexity cannot be a predictive science. And finally, complexity theory is about systems that have the capacity to change but are also bounded by rules that facilitate the evolution of even more complex arrangements, a very suggestive parallel to Hayek's theory of the evolution of rules of social order.

The overlap between complexity theory and Hayek’s theory of spontaneous social order is more than a surface similarity, however. Indeed, given the way in which Hayek’s ideas on the subject emerged, it is reasonable to argue that Hayek’s theory of spontaneous market order was a verbal description of a complex, adaptive social system that at least partially drew its inspiration from the early scientific literature that eventually led to complexity theory.

Hayek on the economics of central planning

It is now well known that Hayek was inspired to develop his theory of spontaneous social order as a consequence of his involvement in the debate over the economic calculation under socialism. The main issue under consideration was whether or not a socialist system could arrive at economic prices without private property and market exchange. A variety of solutions to the problem were offered that essentially relied on conventional economic theory to show how prices could be determined either mathematically, statistically or through a process by which the central planners could iterate toward a "solution" by trial and error. To conventional economists, the economic problem of socialism was solved as long as it could be shown that the equilibrium prices were not logically inconsistent with socialist institutions.[Vaughn, 1980, 1994; Lavoie,1985]

To Hayek, the so-called solutions to the problem of making rational decisions in a socialist economy did not even identify the problem correctly, let alone solve it. The nub of his criticisms of socialist plans all concerned the problem of knowledge: how could planners ever know enough to direct and coordinate the actions of all of the many participants in an economy? Saying that solutions were mathematically consistent, Hayek argued, was not the same as saying that they were applicable to the real world of individual actors with heterogeneous, dispersed and imperfect knowledge. Market economies function because individuals are able to plan their own actions based on their local knowledge of "time and place" and to revise their own plans in light of new knowledge. The price system is the means by which individuals are able to coordinate their actions with one another despite their limited knowledge. As a consequence, market exchange indirectly enables an economic system to benefit from far more knowledge than could ever be employed by a central planner.

Implicit in Hayek’s criticisms of socialist planning was a criticism of the naive manner in which economists at the time were attempting to apply Walrasian general equilibrium theory to redesign the institutions of society. General equilibrium theory presumes that all knowledge is given and known equally to everyone. If that were the case, central planners would have relatively little difficulty in calculating shadow prices to help them direct resources to their highest valued uses. Hayek, however, argued that the real problem was not what to do when the planner has perfect knowledge; it was rather how to make economic decisions knowledge was not given to any one person. The problem facing society, he argued was, "How can the combination of fragments of knowledge existing in different minds bring about results which, if they were to be brought about deliberately, would require a knowledge on the part of the directing mind which no single person can possess?" [1948,p.54] Markets are the result of a vast number of individuals pursuing their own ends who must make decisions with only partial knowledge of the relevant facts. The problem facing the economist is to explain how individual plans can be coordinated so that each person can best achieve his purposes in conjunction with the actions of others. Conventional economics simply did not address this question.

While Hayek’s arguments were not dismissed out of hand by his colleagues, neither were they considered decisive critiques of the economics of socialism. Even economists who agreed with Hayek’s political conclusions did not believe the knowledge problem would present serious problems for socialist planning.[Knight, Schumpeter] In retrospect, it seems apparent that Hayek’s critique was considered of minor importance because he was implicitly struggling to articulate a view of a market economy that did not fit well within conventional general equilibrium theory. It is no wonder, then, that Hayek turned his attention to investigating the methodological and philosophical foundations of his understanding of market economies. What emerged in these methodological writings was a set of ideas that points the way to a theory of the economy as a complex system.

The theory of complex phenomena

Hayek’s methodological essays date from the mid 1940's up until the early 1960's. In these methodological works, one theme that Hayek develops over and over is the peculiar nature of a social system that has a coherence that seems to be the outcome of a single plan but in fact is the unintended consequences of the actions of many independent agents operating separately. In The Counter-Revolution of Science,[1952] for instance, Hayek calls attention to the undesigned nature of the outcome of human action [1952, p.38-39] and argues that a social theory must explain how individual actions can lead to unintended collective outcomes. He invokes both Adam Smith and Carl Menger as social scientists who understood how "spontaneously grown institutions" could develop as a by-product of human action yet appear to be created for a purpose. [1952,p.83]

One characteristic of these unintended orders is that they emerge from the actions of a large number of separate variables which means that "The number of separate variables which in any particular social phenomenon will determine the result of a given change will as a rule be far too large for any human mind to master and manipulate them effectively."[1952, p.42] As a consequence, the scientist will rarely be able to do more than explain "the principle on which certain phenomena are produced." [1952, p.42] Hayek points out that "explanation of the principle" is not confined to social science, but is also applicable to evolutionary biology. One can explain the relationships between the variables, describe a process after the fact, but cannot predict precise outcomes. In economics, he argues, the best example of explanation of the principle is Walrasian general equilibrium. Hence, we see Hayek’s objection to a socialist economics that relies on general equilibrium to control and predict supported by a general principle of what is theoretically possible in a certain class of sciences: general equilibrium is only suitable for explaining the principle by which prices and commodities are related to each other in a market economy. By implication, it is not a suitable tool to use to direct economic activity itself. [1952,p.43]

Hayek’s notion that in some sciences, "explanation of the principle" is the best that can be achieved appears again in an article written in 1952, "Degrees of Explanation." Here, he specifically links explanation of the principle to the complexity of the phenomenon to be explained and argues that as science progresses in the explanation of complex phenomena, explanation of the principle may become the rule rather than the exception. Of particular importance for our argument, is his statement that "Certain developments of recent years, such as cybernetics, the theory of automata or machines, general systems theory, and perhaps also communication theory, seem to belong to this kind"[1952b, p.20] Each of these theoretical subjects contributed in some way to modern complexity theory. Obviously, as Hayek was struggling to articulate the nature of a social order, he was looking to these related fields to illustrate his understanding of a complex system.

The influence of the precursors to complexity theory is even more pronounced in Hayek’s 1964 paper, "The Theory of Complex Phenomena."[Reprinted in Hayek, 1967] There, Hayek describes a set of attributes for complex phenomena that is identical to some of the attributes of complex systems articulated by theorists such as John Holland and Stuart Kauffman. Hayek’s main argument, again, was that some phenomena are so complex that models at best can serve to explain past action and to predict patterns of outcomes, but cannot predict individual events. In particular, he specified evolutionary biology and economic systems as examples of complex phenomena.

Systems are perceived by human beings as patterns of events that require explanation. The complexity of a system, Hayek argued, depends upon "the minimum number of elements of which an instance of the pattern must consist in order to exhibit all the characteristic attributes of the class of patterns in question." [1967:25] The more related elements necessary to describe a system, the more complex it is. Complex systems, moreover, demonstrate "emergent properties" [1967, p.26] that is, the system has characteristics that cannot be simply reduced to an account of its individual parts. There appears to be a chain of "increasing complexity" found in nature, ranging from the simplest inanimate systems to more complex biological systems to the most complex of all, human social systems.

Once again, Hayek took evolutionary biology as his prime example of a complex phenomenon to illustrate his point that the exact outcome of evolution depended upon relationships between an overwhelming number of variables, the exact relationships among which could never be fully specified. Similarly, theories of social structures are also so complex that they cannot be predictive in the conventional sense. They can, however, explain particular patterns of action and rule out impossible futures.

Again, as in his previous essay, Hayek uses Walrasian general equilibrium as an example of a complexity system in social science. General equilibrium describes a particular pattern of price relationships more or less observed in the real world but the theory itself can never be predictive of actual prices because the initial conditions can never be fully specified. The primary value of general equilibrium theory, he argued, was not to predict the future course of events, but only to provide a general description of a particular kind of order.

While Hayek’s description of complex phenomena is much like later accounts of complex adaptive systems, his use of general equilibrium as an example from economics is poorly chosen. It is true that Walrasian general equilibrium systems are composed of a large number of independent agents, but the relationship among those agents is really quite simple. Contrary to modern complex, adaptive systems, in general equilibrium, the agents themselves never interact with each other, instead simply maximizing their own objective functions subject to parameters known to all agents. Because the parameters are available to all alike, each agent essentially has global knowledge of the "true" value of the solutions set. Further, the equations that represent the agents must be linear if a unique solution is to be found. This means that general equilibrium systems can in principle be solved for an optimum using linear programming techniques as long as the equations are fully specified.

By focusing solely on the number of variables in a system and the difficulty of specifying the equations as the marks of a complex system, Hayek did not identify the defining features of modern complex adaptive systems: non-linearity of the elements and the path-dependent interactions among them. This is surprising considering that Hayek’s verbal descriptions of the economic order were very much in the spirit of modern complexity theory. Further, many of Hayek's later criticisms of general equilibrium amounted to attacks on the "linearity" of the assumed relationships even more than on the difficulty of specifying the initial conditions. Indeed, Hayek's whole later emphasis on the process of learning in a market suggests non-linearity and path dependency. Why, then, did he use general equilibrium as an example of a complex phenomenon? The obvious reason is that at this point in his intellectual journey, Hayek had no other fully developed model than general equilibrium for describing the contours of an economic system. It was only in his subsequent writings as he worked out his theory of the market order that he abandoned all references to general equilibrium.

Despite the inaptness of his illustration of general equilibrium as a complex system in the modern sense, there is no doubt that Hayek was at the time struggling to articulate an understanding of the market order as a complex system in the modern sense. As we have seen, he was deeply immersed in the early literature that gave rise to complexity theory. In "The theory of Complex Phenomena," he cites von Neumann's important article on "The General and Logical Theory of Automata," a classic contribution to the theory or artificial intelligence, L. von Bertalanffy on the complexity of biological systems, Lloyd Morgan on the nature of "emergent" properties, Steven Toulmin on the ability of biology to rule out possible futures, and Noam Chomsky on the method of linguistics as related to economics. Hayek’s familiarity with this literature, revealed in much of his methodological work after 1952, is important since at this time he was beginning to work out his evolutionary theory of social rules. While the major influence on Hayek’s social theory was probably biological evolution, biological evolution is itself one of the most convincing examples of a complex adaptive system in the modern sense.

Hayek and spontaneous market order

Most of Hayek’s work during the 1960's was preparatory to writing his three volume masterpiece, Law, Legislation and Liberty. The lynchpin of his "statement of the liberal principles of justice and political economy was his notion of spontaneous order. Spontaneous orders are social patterns that emerge as "the result of human action but not of human design," that is, "from the bottom up" through the actions of individuals directed to their own purposes. The spontaneous social order is unplanned in the sense that it was not designed by some higher intelligence or some central planner. The reason that an order can emerge from the self-directed actions of individuals is that individual actors are not only purposeful, but they are also rule followers.[1973,pp.38-46] It is the rule-following behavior of human beings that generates the order that makes society possible. Even more, the spontaneous social order is an evolutionary process in that rules that make society possible result from a selection mechanism that rewards groups who follow more successful rules [1973,pp.44; 1967, pp.68-81]. These rules consist of law, customs and habits (the institutions of a social order) that emerge as an unintended consequence of individual action - "emergent properties" in the parlance of complexity theory.

Hayek regarded the economy (or catallaxy, as he preferred to call it [1976,p.108]) as a special case of spontaneous social order, one that was guided by the laws of property, tort and contract. That is, these laws are the rules that agents must follow to permit the spontaneous order to emerge. As in his earlier economic essays, Hayek emphasized the dispersion and heterogeneity of knowledge that made markets necessary, and argued that coordination of the system comes about through competition of agents for profits aided by the price system. Unfortunately, apart from his insistence on the nature of the catallaxy as the interactions of individual agents who have no common goal, his account of "the game of catallaxy" [1976, p.115] is too limited of purpose to give a complete account of the market order as a complex, adaptive system. However, by piecing together Hayek’s descriptions of a market economy from his various writing, it seems clear that his understanding of markets is much closer to a complex, adaptive system than it is an example of Walrasian general equilibrium.

A. As in all complex adaptive systems, a catallaxy is composed of many separate agents pursuing their own advantage. There is no objectively determined hierarchy of aims.[1978, p.109]

B. There is no globally available knowledge: individuals are always groping their way around their local environments with limited knowledge of "time and place." [1948:80] Hence, the economic problem is one of interaction among independent agents each seeking their own optimum; it is not simple global maximization problem.

C. Because "...one person’s actions are the other person’s data,"[1948:p.38] agents learn to revise their plans (or strategies) to better achieve their purposes. The result is that agents learn through their experiences and hence become more adapted;[1948: p.46] that is, individuals learn to improve their ability to create wealth by learning what works and what does not. They learn through trial and error how to exploit niches in their environments.

D. This leads to the creation of new structures or "emergent properties" in the form of new products, new technologies, new firms, new market customs.[1948: pp. 92-106] Each of these emergent properties cannot be explained solely by the individual actions that led to them. Further, these emergent structures permit the development of more and more complex and specialized forms and institutions. A modern industrialized economy is a veritable web of interlocking and supporting markets and institutions.

E. Finally, the constant change that agent learning brings about means that catallaxies are path-dependent. What people learn depends upon what they know and what kind of problems they face. The existing capital stock greatly influences the shape of new investment just as the kinds of tools and production techniques available in any one time influence the specific nature of technological innovation that occurs.[1960:27]

It seems evident that all of these elements add up to a reasonably complete description of the catallaxy as a complex, adaptive system.

Potential uses of complexity theory for Austrian economics

Even if it is true that Hayek’s account of the catallaxy was a verbal statement of a complex, adaptive system as the term is understood today, does it matter? Specifically, is there anything important to be gleaned from studying this relatively new science, or are the verbal analyses Austrian have been content to employ sufficient to do Austrian economics?

While many may remain skeptical [See Boettke, 1997], I am cautiously optimistic that the science of complexity, by clarifying the characteristics of non-linear, adaptive systems may prove to be an aid to articulating a more Hayekian understanding of the market order. For instance, the mature theory of complex adaptive systems can help support Hayek’s central argument against central planning.

Consider the "mathematical solution" which held that all one needed was to set up a system of simultaneous equations to generate equilibrium prices that could guide planners.[Dickinson, 1933] At the time of the economic calculation debate, computers were not available to attempt to set up and solve those equations, so even the socialist sympathizers agreed that such a scheme was "practically" impossible, at least for the immediate future. Oskar Lange’s "trial and error" solution to the problem of factor pricing was a fall-back to achieve the same goal without computers.[Lange and Taylor, 1938] However, Lange never gave up on the possibility that one day, computers could be used to direct a centrally planned economy, making his clumsy trial and error solution obsolete.[Kohler,1997] The science of complexity can finally put that fantasy to rest, and at the same time, vindicate Hayek’s insight.

We recall that computer scientists learned from experience that non-linear, many equationed systems cannot be solved by programming them "from the top, down." Indeed the closest computers can come to a solution is to essentially try out solutions and comparing them to each other. Even then, the method of "comparing" the solutions that works best is an indirect one. That is, computer scientists approach solutions to these complex problems by devising artificial agents who are given simple, but varying decision rules, providing specific pay-offs to the their various actions and then allowing the agents to compete with each other for computer time. In a process remarkably like economic agents attempting to make a profit, the most "successful" artificial agents get more time as they come up with better and better solutions to the specified problem. The point is that to solve much simpler problems than presented by a vast economy, computer programmers have had to simulate market-like activities to come up with workable solutions. Hence, rather than computers substituting for markets to run an economy, markets have had to be incorporated into computer programs to solve problems far less complicated than are presented by real economic systems. To duplicate the relative efficiency of a market economy would require a program as complex as the market itself and contain agents as intelligent as real human beings. Even then, it could not be used to predict and direct so much as to explain. It seems that when Hayek tried to claim that the "mathematical solution" of optimizing a social objective function simply did not come to grips with the real problem faced by markets, he was even more correct than he realized.

The challenge to today’s Austrians, however, is no longer the threat of central planning. Today, the supposed pervasiveness of market failure is the justification for government interventionism. Unfortunately, models of complex systems can incorporate positive feedbacks and path-dependencies that appear to demonstrate inefficient market results that seem to cry out for government remedy. Brian Arthur’s work on network externalities and technological lock-ins [1989]is one important case in point.[See also, Krugman] Yet, if we agree with the complexity theorists that economies are more like non-linear systems than linear ones, what is an Austrian to make of these proofs of new ways in which markets can fall short of the neo-classical ideal?

This is one area in which complexity theorists can learn from Hayek. Perhaps the simplest answer is, "Why should the neoclassical ideal be taken seriously when one understands the real nature of a complex market system?" Perfect, fully complete markets is an analytic fiction that does not apply to the real world just as it did not apply to the problem of socialist planning. Market "failures" are only failures to achieve the result of an inapplicable model. The salient point is that individual actors, operating in a regime of property and contract, are capably by trading with one another to create an ever growing amount of wealth despite their limitations. The Hayekian question to ask is not, how many ways might markets fail, but why, as a matter of empirical observation, do they so often succeed? Or, to rephrase that in the parlance of complexity theory, why do markets so often appear to act like simple linear systems when non-linearity seems to be a more realistic assumption for human interaction?

Recently, Stephen Margolis commented that the useful aspect of Brian Arthur's work on path-dependency and lock-ins was not to point out a potential market failure, but to force us to ask how entrepreneurs deal with the problem. If lock-ins and network externalities can potentially exist, but we find few or no real world examples, that must mean that entrepreneurs have found ways for the late comers to even up the playing field with the first entrant in a new market. By identifying a potential market problem such as network externalities, we perhaps explain behavior directed toward solving the problem that might not have been comprehensible before. For instance, trial discounts may be a way of overcoming a lock-in while bundling of services might be a way of overcoming a network externality. People are not perfect, but they do search for ways to overcome their limitations. Models that incorporate non-linearities give us more tools to identify the problems that real world institutions have arisen to solve.

This approach has been deliberately followed by Axel Leijunhufvud. Recently, Leijunhufvud has been examining what he calls "out-of-bounds" situations such as hyperinflation, situations he argues are non-linear and characterized by positive feed-backs[1995]. He argues that by analyzing such situations, we can get a better grip on those aspects of the economy we take for granted. His work on high inflation, for example, shows that intertemporal markets of all kinds disappear as inflation increases, belying the neoclassical prediction that markets would find ways to contract around increased uncertainty about future prices. This points to the importance of predictable institutions for intertemporal planning, and predictable monetary value in particular. Furthermore, his analysis suggests an important new theory of how price stability in particular markets is necessary to extend planning ever further into the future.

Both Margolis's comment and Leijonhufvud's recent work suggest an appropriate use of complexity theory. At the very least, at this stage of its development, it can serve as a foil to investigate the characteristics of real economic systems. That is, it may well provide a alternative for Mises's Evenly Rotating Economy that allows us to address more sophisticated market phenomena than his simple model. By providing a set of possible undesirable outcomes from assumed non-linear relationships, economists are directed to searching for the particular institution or practice that individuals have discovered to solve the problem.

Additionally, by articulating a set of common characteristics of all complex, adaptive systems, complexity theory can help sharpen the Austrian analysis of the market process. By describing the processes by which other systems adapt and change, it can offer an analogy to be adapted to the particular case of social change. Certainly, a theory that incorporates learning and change, the evolution of new forms and increasing variety has far more to offer economics than any previously employed scientific analogy. Like all analogies, comparisons of economies to the artificially created complex adaptive system of computer simulations will be incomplete, and must be handled with care. But even incomplete analogies are often instructive. As long as Austrians don't repeat the neoclassical vice of thinking the analogy is equivalent to the real world and trying to change the world to fit the model, we can cautiously explore gains from trade with the new science of complexity.

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