Reviewed by
Piergiuseppe Morone
University of Foggia, Dipartimento di Scienze Economiche, Matematiche e Statistiche
Complexity theory is undoubtedly relevant for social sciences and has gained momentum as a valuable research stream over the last decades. Economists and other social scientists realised the importance of complexity, observing the growing relevance of inter-relationships among the components of social systems - as well as their relationships with the environment - in determining collective behaviours. This characteristic of complex systems has proved to be incompatible with the application of traditional mathematics, typically used in economics, hence calling for the use and development of new classes of combinatorial mathematics and population-level stochastic processes, in conjunction with computer modelling (Arthur, Durlauf and Lane 1997). Frenken's book (which enriches Edward Elgar's collection on Innovation, Evolution and Institutions) applies complexity theory to the issue of innovation, providing new computational insights on the emergence of complex architectures and on the occurrence of technological paradigms. The book is divided into two parts: a first part in which the theoretical debate is presented and developed along the lines of evolutionary models of fitness landscapes (see below); and a second part in which the author completes his research by providing several case studies for a range of technologies. The two parts nicely complement each other, providing the reader with a clear picture of a relevant portion of complexity theory and its possible application to evolutionary economics.
Stuart Kaufmann's NK model, widely discussed in the second chapter of the book, marks an important step in the direction of understanding innovation and technology evolution within a complexity theory framework. The basic idea (which is borrowed from early studies on genes that self-organise the development process of an organism) is that the degree of complexity of a system depends directly on its components' interdependence, called epistatsis. Interdependence of components implies, in turn, that a single component's mutation affects differently (and possibly with opposite signs) other components. Hence, a general improvement in the system as a whole is obtained only if the improvement in one of its traits outweighs the negative side-effects observed in other traits.
This finding, first observed for biological organisms, also applies to systems intended for the development of artefacts. Indeed, Frenken uses this theoretical framework to investigate firms' innovation behaviours in an evolutionary context. As put by the author: "[a]pplying complex system theory, originally developed in the context of biology and computer science, we can approach a range of innovation topics in a novel and systematic manner".
Following Kaufmann's NK model theory, Frenken conceptualises complexity with respect to the number of linkages (epistatic relations) among system components. Hence, model complexity arises from the fact that the number of possible combinations is an exponential function of the number of elements. The concept of fitness landscapes is then introduced to exemplify the search process which takes place in such environment. If agents operating in a fitness landscape apply a search strategy based on a myopic trial-and-error process - i.e. randomly mutating the single elements - this will eventually lead them to local optima (by means of what Kauffman calls adaptive walk). The number of local optima is directly related to the degree of epistatsis of the model (K): the larger and more complex the system is, the higher is the probability of ending up in a local optimum rather than reaching the global optimum.
Being locked in local optima could be avoided only by performing an exhaustive search which requires evaluating all possible combinations between elements (this is also called global trial-and-error). However - as put by Frenken - this search strategy is "the most inefficient [...] in terms of costs of search". Nonetheless, between the global and the myopic trial-and-error search strategies there is a whole range of possibilities which trade-off the effectiveness of the search performed with its cost.
Ultimately, a designer aiming at innovating an artefact could, in fact, mutate more than one element at the same time, hence increasing the scope of her search (i.e. enlarging the search distance, N). This searching strategy allows designers to move from one local optimum to another by means of 'long jumps' which, eventually, might lead to the global optimum. Note that the global optimum is more easily reached (without engaging in an exhaustive search) if the system is decomposable (i.e. it is divisible in subsystems such that all epistatic relations are located within subsystems rather than between subsystems) or near-decomposable (i.e. where subsystems are loosely linked).
After having illustrated its theoretical basis, the author presents a generalisation of the model (chapter three) which allows for non-squared matrix, i.e. a system characterised by any number of elements and any number of functions. This generalisation of Kaufmann's NK model was first proposed by Altenberge (1994) and here it is instrumentally presented to lead the reader towards the fourth chapter where an original evolutionary model of technological paradigms is developed. Specifically, in this chapter the author aims at filling a gap in the literature on product life cycle which, in spite of its extensiveness, has failed - in Frenken's view - to account for the innovation dynamic that occurs during the life cycle of an industry.
In the evolutionary model presented in chapter four, path dependency is an endogenous feature which emerges from the "constructional selection" of the evolving complex system. Hence, standardisation is not determined by increasing returns (as it occurs in David 1985 or Arthur 1989), but by the progressive reduction of the searching space (design space) as the artefact design converges to a fixed set of core components and innovation shifts towards peripheral components. Constructional selection is, therefore, a way of dealing with "the tyranny of combinatorial explosion" as put by Stan Metcalfe (1995) and reported in this book by the author.
A noteworthy insight of this model is that it allows accounting for the anomaly first empirically observed and pointed out by Gort and Klepper (1982), i.e. that the rate of innovation does not fall as dominant design emerges. As clearly stated in chapter four, the appearance of a dominant design simply shifts innovation activities from core to the peripheral components of a technology.
In the second part of the book, dedicated to the empirical case studies, Frenken first introduces entropy statistics (chapter five) which are used to trace the evolution of dominant designs. Along Weitzman's measure of diversity and hedonic price regressions, entropy is employed to study the evolution of steam engines, trajectories in aircrafts and helicopters, as well as the advent of portable computers. This happens respectively in chapters six, seven and eight.
In these chapters, by means of case studies and empirical analysis, Frenken reflects upon relevant concepts such as non-linearity of innovation processes, speciation and co-evolution; this provides the reader with strong evidence in favour of the view that technological innovation is the result of evolution in complex and interdependent systems.
To conclude I should mention that reading this book is enjoyable as the author never indulges in technicalities for the sake of them. In spite of the 'complexity' of the topic, the prose is kept simple and continuous references to exemplifications guide the reader through the book. In my view, these elements make the book a good manual for postgraduate students that approach the topic for the first time, as well as a valuable reference for scholars and researchers.
Possible extensions of this book would include the study of other complex systems as well as different complex models. As acknowledged by the author himself, three further possible lines of research could be co-evolutionary models, industry life cycle models and the Schumpeterian idea of variety and economic development[1]. I share the author's view that these are all promising lines of research.
As a last remark, I would like to point out that other approaches to complexity theory exist in the literature. I am aware that this is beyond the scope of this book which relates exclusively to biological models and fitness landscapes literature; however, it might be worth mentioning here the potential novelty in addressing and modelling complex systems offered by multi-agent based simulation (MABS) models. Recently, Bruce Edmonds and Scott Moss (2004) raised the question on whether a model should be kept as simple as possible (the so-called KISS approach - Keep It Simple Stupid) or as descriptive as possible (what the authors have labelled KIDS - Keep It Descriptive Stupid). This question intrinsically relates to the issue of complexity. In fact, as put by Edmonds and Moss, "[g]iven that much that we study is complex, it would be very surprising if it always turned out to be the case that the models could be simple". Moreover, MABS "not only enables the KIDS approach but epitomises it".
Multi-agent based simulations improve descriptive accuracy and establish a strict link between theorising and empirical observation. In doing so, they serve as a tool to develop models which relate as strongly as possible to the target domain: "actors or agents in the target domain are represented by agents in the model and communications are represented by messages. That is MABS allows and facilitates a more direct correspondence between what is observed and what is modelled". Note that implementing the KIDS philosophy requires inverting the research design as it is presented in this book: not introducing the models first in a theoretical section but developing them after the analysis of the cases (where the descriptive accuracy is extracted).
In areas dominated by complex phenomena (such as social systems) MABS models, based on KIDS approach, represent a new promising tool for scientific computational (rather than analytic) studies. This brings us back to the methodological issue raised at the beginning of this review where, following Arthur, Durlauf and Lane, we invoked the development and use of new mathematical and computational tools in order to address complexity.
Notes
ReferencesALTENBERG L (1994) Evolving better representations through selective genome growth. In D. Schaffer, H.P. Schwefel and H. Kitano (Eds.) Proceedings of the First IEEE Conference on Evolutionary Computation, Orlando, Florida, USA: 182-187.
ARTHUR WB (1989) Competing technologies, increasing returns and lock-in by historical events, Economic Journal, 99: 116-131.
ARTHUR WB, DURLAUF, S and LANE D (1997) Introduction: The Economy as a Complex Evolving System. In(Eds.) The Economy as a Complex Evolving System II. Santa Fe Institute, Santa Fe and Reading, MA: Addison-Wesley.
EDMONDS B and MOSS S (2004) From KISS to KIDS: An 'anti-simplistic' modelling approach, MAMABS 2004, New York.
DAVID P (1985) Clio and the Economics of QWERTY, American Economic Review, 75, 2: 332-337.
GORT M and KLEPPER S (1982) Time-path in the diffusion of product innovation, Economic Journal, 92: 630-53.
LEVINTHAL DA (1997) Adaption on rugged landscapes, Management Science, 43: 934-950.
METCALFE JS (1995) Technology systems and technology policy in an evolutionary framework, Cambridge Journal of Economics, 19: 25-46
SORENSON O (2003) Interdependence and adaptability: organizational learning and the long-term effect of integration, Management Science, 49: 445-463
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