《Innovation, Diversity and Diffusion：A Self-Organisation Model》1 Silverberg-1988-Innovation, Diversity and Diffusion-A Self-Organisation Model

The diffusion of new products and new processes of production within and between business enterprises is clearly one of the fundamental aspects of the process of growth and transformation of contemporary economies It is well known that the diffusion of new products and processes takes varying lengths of time: some economic agents adopt very early after the development of an innovation while others sometimes do it only after decades

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The Economic Journal, g8( December 1988),1032-1054 Printed in Great britain INNOVATION, DIVERSITY AND DIFFUSION: A SELF-ORGANISATION MODEL Gerald Silverberg, Giovanni Dosi and Luigi orsenigo The diffusion of new products and new processes of production within and between business enterprises is clearly one of the fundamental aspects of the process of growth and transformation of contemporary economies It is well known that the diffusion of new products and processes takes varying lengths of time: some economic agents adopt very early after the development of an innovation while others sometimes do it only after decades Moreover, during the diffusion process the competitive positions of the various gents(adopters and non-adopters)change. So do the economic incentives to adopt and the capabilities of the agents to make efficient use of the innovation Finally, the innovation being adopted also changes over time, due to more or less incremental improvements in its performance characteristics which result in part from its more widespread use. Contemporary analysis of diffusion has been essentially concerned with the following questions:(a)why is a new technology not instantaneously adopted by all potential users?(i.e. what are the 'retardation factorspreventing instantaneous diffusion? ),(b)how can the dynamic paths of diffusion be represented? and(c)what are the relevant variables driving the process? However, innovation diffusion has rarely been formally treated as part of a more general theory of economic dynamics in which diversity of technological capabilities, business strategies, and expectations contribute to shape the evolutionary patterns of industries and countries(a remarkable exception is the evolutionary approach developed in particular by Nelson and winter (I982) who, however, are more concerned with the general features of industrial dynamics than with the specific characteristics and implications of the diffusion In this work, we shall analyse the nature of diffusion processes in evolutionary environments characterised by technological and behavioural diversity amongst the economic agents, basic uncertainty about the future, learning and disequilibrium dynamics shall identify some fundamental characteristics of technology innovation and diffusion which, we suggest, must be accounted for in theoretical models. Second, against this background, we shall briefly review s We gratefully acknowledge co ts on an earlier paper on which this work is participants at the International Conference on Innovation Diffusion, Venice, I7-21 March 1986, and onymous referees and Associate Editor, The work of one of us(Silver as partially supported by a grant from the Deutsche Forsch haft while the research of one of us(Dosi) has been part of the activities of the Designated Research Centre, sponsored by th R C. at the Science Policy Research Unit(SPRU), University of Sussex [1o32

DEC I INNOVATION AND DIFFUSION I033 what we consider the major achievements and shortcomings of the current models of innovation diffusion. Third, we shall present what we call a 'self organisation' model of innovation diffusion, that is, a model whereby relativel ordered paths of change emerge as the(partly)unintentional outcome of the dynamic interactions between individual agents and the changing charac- teristics of the technology. Fourth, the main properties and simulation results of the model will be discussed . CHARACTERISTICS OF TECHNOLOGY AND DYNAMIC INDUSTRIAL ENVIRONMENTS A renewed interest in the economics of innovation over the last two decades has brought considerable progress in the empirical description and theoretical conceptualisation of the sources, characteristics, directions and effects of technical change. We review these topics in Dosi(1988). Here, it suffices to summarise some of the major findings directly relevant to the diffusion of nnovations concerning the nature of technology and the characteristics of firms and innovative environments a) Technology-far from being a free good-is characterised by degrees of appropriability, of uncertainty about the technical and, a fortiori commercial outcomes of innovative efforts, of opportunity for achieving technical advance, of cumulativeness in the patterns of innovation and exploitation of technological know-how and hardware, and of tacitness of the knowledge and expertise on which innovative activities are based. Particular search and learning processes draw on technology-specific knowledge bases, related to both freely available information(e.g. scientific results)and more ' and tacit skills, experience and problem-solving heuristics embodied in people and organisations b)Technologies develop along relatively ordered paths(or 'trajec ctories”) shaped by specific technical properties, search rules, 'technical imperatives and cumulative expertise embodied in each"technological paradigm'(cf.Dosi ( 1984); for similar arguments see Nelson and Winter(1977), Sahal(198 1985), Arthur (1985), Metcalfe (1985)and within somewhat different perspectives, Atkinson and Stiglitz (196g )and David(1975)). Relatedly, Winter(I984)defines different 'technological regimes,accor to whether the knowledge base underpinning innovative search is prim Universal, and thus external to individual firms, or, alternatively, is primarily"localand firm-specific (c) As a consequence of(a) and(b), diversity between firms is a fundamental and permanent characteristic of industrial environments undergoing technical change(see also Metcalfe( 1985)on this point). Inter-firm diversity(even within an industry) can fall into three major categories First, there are technological gaps related to different technological capabilities to innovate, different degrees of success in adopting and efficiently using product and process innovations developed elsewhere, and different costs

I034 THE ECONOMIC JOURNAL DECEMBER of production of output. In Dosi (1984)we define these forms of diversit -y technological asymmetries, meaning unequivocal gaps between firms which can ranked as better'and worse'in terms of costs of production and produc characteristics Second, diversity relates to differences between firms in the procedures, input combinations and products, even with roughly similar production costs(on this point, see Nelson(1985). Similarly, firms often search for their product innovations in different product-spaces and concentrate their effort on different sections of the market Let us call this second set of sources diversity technological variety, meaning all those technological differences hich do not correspond to unequivocal hierarchies ('better'and worse technologies and products Third, one generally observes within an industry (and even more so betwe industries) significant differences in the strategies of individual firms with respect to the level and composition of investment, scrapping, pricing, R d etc. Let us call these differences behavioural diversity Evolutionary processes in economic environments involving innovation and diffusion are governed to different degrees by selection mechanisms and learning mechanisms. Selection mechanisms tend to increase the economic dominance (e.g. profitability, market shares) of some firms with particular innovation characteristics at the expense of others. Learning mechanisms, on the other hand, may both spread innovative/imitative capabilities throughout the (possibly changing) set of potential adopters and reinforce existing disparities via cumulative mechanisms internal to the firm e Learning processes generally occur via (a) the deveopment of intra-and inter-industry externalities'(which include the diffusion of information and expertise, interfirm mobility of manpower, and growth of specialised services) (6)informal processes of technological accumulation within firms(of which learning-by-doing and learning-by-using are the best known examples of such internalised externalities); and (c) processes of economically expensive search 很R&D After a brief survey of the current state-of-the-art in the theory of innovation diffusion, we shall present a model which, in our view, makes a serious attempt to incorporate some of these features of innovative environments in a novel, yet consistent and realistic way II. DIFFUSION MODELS: RESULTS AND LIMITATIONS Three basic approaches dominate current economic thought on innovation diffusion (cf. Stoneman (I983; I986), Arcangeli(I986)). First, the line of enquiry pioneered by the seminal work of Mansfield(I961; 1968),and Griliches(1957) tries to identify the empirical regularities in diffusion paths, typically represented by S-shaped curves. In Mansfield's'epidemic'approach diffusion is generally found to be pushed by the expected profitability of the innovation and driven by the progressive dissemination of information about

INNOVATION AND DIFFUSION its technical and economic characteristics. Thus, diffusion is interpreted as a process of adjustment to some long-term equilibrium contingent upon learning Empirical work on diffusion, however, whilst confirming the role of profitability in adoption decisions, has shown that differences in the characteristics of innovations, of product mixes, and of the potential adopters are also key factors in the diffusion process(see, for example, Nabseth and ray (1974), Gold( 1981), Davies(I979), David(I975) These findings, together with theoretical considerations about the crudely mechanical nature of epidemic diffusion models, lend support to a second approach, namely one based on'equilibrium diffusion models'. Here, diffusion is seen as a sequence of equilibria determined by changes in the attributes of the innovation and the environment(see David(1969), Davies (1979), Stoneman and Ireland Ireland and Stoneman(1986), David and Olsen (Ig84), Reinganum )). This approach has undoubtedly provided important insights into diffusion processes. Amongst other things, it has shown the importance of (i)differences(such as size) between potential adopters;(i)the interactions between the supply decisions of the firm producing innovations and the pace of their adoption; (ii)the technological expectations of suppliers and adopters; (iv) the patterns of strategic interactions amongst both suppliers and adopters; (v) the market structure in both the supplying and using industries. However, these results are generally achieved at a high theoretical price. Radical uncertainty is de facto eliminated and maximising behaviour is assumed. 2 The analysis is often undertaken in terms of the existence and the properties of equilibria, while nothing is generally said about adjustment processes. Information about the techno-economic charac teristics of the technologies is generally assumed to be freely available to all agents. The nature of 'technology'is radically simplified and assumed to be embodied in given technical features of production inputs o A third approach is explicitly evolutionary and represents the diffusion of new hniques and new products under conditions of uncertainty, bounded rationality and endogeneity of market structures as a disequilibrium process (Nelson, 1968; Nelson and Winter, I982; Metcalfe, I985; Silverberg, I984 The model that follows is in this evolutionary tradition, and thus allows for isequilibrium processes, endogeneity of market structures, etc. It also explicitly incorporates those assumptions ofequilibrium'diffusion models which capture important empirical characteristics of innovative environments mentioned earlier, such as the relevance of expectations and differences between agents, as the transition between 2 To be precise, in Davies'original model adoption are based on rules of thumb explicitly d in terms of 'bounded rationality. Ye See also Eliasson(1982; 1986). On the connection to empirical ana Gort and Klepper(1982). Gort and Konakayma(1982)and Levin et al. (1985)

1036 THE ECONOMIC JOURNAL IDECEMBER well as some features implicit in Mansfield-type models, such as imperfect nformation and as ymmetric technological knowledge.d IIL A SELF-ORGANISATION MODEL OF THE DIFFUSION OF INNOVATIONS AND THE TRANSITION BETWEEN TECHNOLOGICAL JECTORIES In two previous papers, one of the present authors(Silverberg, I984; I987 attempted to demonstrate the relevance to economic theory of the self- organisatio proach to dynamic modelling pioneered by Eigen, Haken Prigogine and others. In essence the argument proceeds from the observation that in complex interdependent dynamical systems unfolding in historical, i c irreversible time, economic agents, who have to make decisions today the correctness of which will only be revealed considerably later, are confronted with irreducible uncertainty and holistic interactions between each other and with aggregate variables. The a priori assumption of an'equilibrium'solutic to this problem to which all agents ex ante can subscribe and which makes their actions consistent and in some sense dynamically stable is a leap of methodological faith. Instead we proposed employing some of the recently developed methods of evolutionary modelling to show how the interaction of diverse capabilities, expectations and strategies with the thereby emerging selective pressures can drive a capitalistic economy certain definite patterns of development Drawing on a dynamic model of market competition with embodied technical progress investigated in Silverberg(I987), we embed the question of diffusion into the larger one of the transition of an industry between two technological trajectories. Choice of technique is no longer a choice between two pieces of equipment with given(but perhaps imperfectly known characteristics, but now involves skills in using them which can be endogenously built up by learning by doing or by profiting from the experience of others, as well as expectations about future developments along the various competing trajectories. As we shall see, the diversity in firms'capabilities and expectations is an irreducible element driving the diffusion process In the sectoral approach taken here industry-level demand is taken as given and growing some exponential rate. Firms command some market share of his demand at any given time, but market shares may change over time as a dynamic response with a characteristic, time constant(reflecting the'freeness of competition and such factors as brand loyalty, information processing and search delays and costs, etc. )to disparities in the relative competitiveness of firm This concept, so dear to close observers of the business scene, has to our knowledge evaded incorporation into a systematic economic theory until now 4 A more detailed discussion of the empirical basis of the hypotheses entering into the model presented below can be found in Dosi et al.(I tional modelling Haken(1983), Nicolis and Prigogine(1977) and Prigogine(1976)

INNOVATION AND DIFFUSION The evolution of market structure is governed in our approach by an equation relating the rate of change of a firms market share to the difference between its competitiveness (defined below)and average industry competitivene averaged over all competing firms in an industry, weighted by their market shares). This equation is formally identical to the equation first introduced into mathematical biology by R. A. Fisher in 1930 and more recently applied in a variety of contexts and studied in considerable mathematical detail by Eigen (1971), Eigen and Schuster(1979), Ebeling and Feistel (I982), Hofbauer and Sigmund(I984), and Sigmund (1986). Our use of this equation differs from most biological applications, however, in that the competitiveness parameters ather than being constants or simple functions of the other variables themselves change over time in complex ways in response to the strategies pursued by firms and feedbacks from the rest of the system. In a systems theoretic sense this equation may be regarded as the fundamental mathematical description of competitive processes. It is worth emphasising the difference between our approach and standard theoretical conceptualisations of com- petition. The latter generally identify the circumstances under which no lative competitive shifts or profits can be realised(impossibility of arbitrage uniform rate of profit, etc )and then assume that the system must always be in or near this state If we denote by fi the market share in percentage of real orders of the ith firm, by Er its competitiveness and by (e>the average competitiveness of all firms in the industry(=EfE, then the evolution of market shares is governed by the following equation =A(E-〈E》 le define the competitiveness parameter as a linear combination of terms reflecting relative price and delivery delay differentials E=-InPe-Alo dd, where Pr is the market price of the ith firm and dd, its current delivery Silverberg (1987) presents a basic dynamic structure for dealing with strategic investment in the face of uncertainty with respect to the future course of embodied technical progress, overall demand and changes in relative competitiveness. In this framework, entrepreneurs are seen as being fully change, so that their decisions, particularly concerning fixed investment, take ccount of and try to anticipate these developments. Decision-making is incorporated on the one hand in certain robust rules of thumb(for the most part feedback rules dealing with oligopolistic pricing and production policies) and' animal spirits in the form of decision rules governing replacement policy the payback period method)and expansion of capacity ('estimates'or guesses of future demand growth corrected by experience). Technical change here to mark

THE ECONOMIC IOURNAI DECEMBER is embodied in vintages, and the resulting capital stocks are not assumed to start in, and in general need not converge to steady-state distributions The capital stock(measured in units of productive capacity) of each firm is represented as an aggregation over nondecaying vintages between the current period t and the scrapping date T(t) K()=K(4,)dr where k,(t, t)is gross investment at time t(in capacity units) K(4,t)=k(,n)if T(o)<t<t and o otherwise This aggregate capital stock may be a composite of different technologies as well as different vintages of a single technological trajectory. A payback calculation is performed by each firm with its desired payback period(which may differ between firms) to determine a desired scrapping date for its capital stock Tar(t) by solving P(D)/(c(a)-c(0)]=b, here P(t)is the price of new capital equipment per unit capacity, c(... )is the unit operating cost at time t of the vintage in question, and b, is the target payback period of the ith firm The actual scrapping date adjusts to this desired date via a first-order catch p procedur T=z max [Au(la-1),o where zu is a rationing parameter between o and I(the ratio of current cash How to desired gross investment) which may arise if the ith firm, due to financial constraints, is not able to finance its desired investment programme fully (otherwise it is I). The amount of capacity scrapped as a result of this decision(as well as a possible desire to reduce overall capacity)is S=kt, T)T Net expansion (or contraction) of capacity is governed by a desired rate r for each fir technologically obsolete equipment should beemingly'self-evident' rules have been applied to decide when 7 In the economics literatu ced by new cquipment, One calls for an old vintage to replacement when unit variable costs exceed the price attained per unit of output. A substantial specialised literature exists, however, dealing with optimal replacement beginning with Terborgh(Terborgh, 1949;see also Smith, 1961). Under suitable assumptions about the rate of future technical progress this leads to the so-called square root rule. k criterion is a reasonable approximation to in this ru calculations to be widely For a discussion of optimal replacement in the evolutionary framework emp ere see Silverberg (987)

THE ECONOMIC JOURNAL DECEMBER The quadratic saturation term is introduced to represent bottlenecks in the production process near the full capacity limit. Delivery delay dd is the ratio of order backlog L to current production y(=uK), and the order backlog governed by the rate equation y (14) where d is incoming orders (=fi X total market demand irms'prices are determined as a dynamic compromise between the desired mark-up on unit costs and relative competitiveness. Since only relative prices are of importance here, we take the logarithm of price variables throughout. Let p, be the log of the ith firm's market price and Pe its desired markup price based on its unit prime costs. Then 内=A1(p4-p)+A8(E-) Pricing licy is regarded as a compromise (depending on the 'degree of monopoly' characteristic of an industry) between strict cost-plus pricing and a concession to the prevailing market price( the geometric mean of all prices weighted by market shares)via relative competitiveness. This structure of pricing allows the changing relative cost structure of firms to be transmitted through the market and makes intelligible such phenomena as price leadership or being under price pressure. Firms at a competitive (in general mostly cost disadvantage are thus forced to lower their prices somewhat to prevent excessive losses of market share, while firms enjoying a competitive advantage are free to realise short-term profits by raising their prices. The ratio of Ag to A, determines to what extent competitive pressures overrule the markup principle(which remains valid, however, at the aggregate level)and enables the model to span the entire range of market structures between pure monopoly and pure competition As the model now stands, with a single vintage structure for each firm, already accounts for the diffusion of new technology in the case in which a unique best practice technology is apparent to all agents(this perspective on diffusion was first introduced by Salter, I962). The process of investment under the assumption of some long-term rate of technical progress implicit in the ayback method ensures that advances in productivity will be continuall incorporated into the capital stock, even if entrepreneurs differ in their assessment of the appropriate payback to use. Thus diffusion of technical progress is already guaranteed by the standard methods of investment policy at this first level of anal However, in order to capture the collective dynamic of advance along different technological trajectories we propose the following additional structure. We compare two technological trajectories representing at any time the maximum productivities attainable in best practice vintages of the respective technologies. We assume that these are both changing at some rate, and that the second technology is always absolutely superior in productivity. Moreover, the relative price/capacity unit of the two technologies may also be 10 For a more detailed discussion of the price interactions to which this system leads se (I987

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