Innovation and competition in complex environments.

SUMMARY

The paper aims to shed light on the relation between technological research, competition and market dynamics, focussing on the role of product modularity. This relation is analysed via qualitative simulation modelling using a simple agent-based model. We define an economic system in which firms compete on the quality characteristics of a certain complex good, in a market where consumers have shown preferences for them. Firms are conceived as bounded rational agents that explore complex product technologies in order to improve their fitness in relation to the selection environment (i.e. the consumers' evaluation of the characteristics of the final good). The architecture of the good produced in the system is characterised by different degrees of modularity (i.e. the lower the correlations between the contributions of the different product components to the final product fitness, the simpler the good's technology and the higher the degree of modularity). On the other hand, the impact of product modularity on industrial dynamics is analysed using a set of quite homogeneous firms.

First, the model yields highly differentiated dynamics for firms that start from similar initial conditions, pointing to the importance of their research strategies. Second, the dynamic patterns obtained show that firms may easily end up in technological lock-in in spite of initial good performance, suggesting that path-dependence could be broken. Third, modularity impinges directly upon market results: a decrease in modularity, by increasing the difficulty in searching the complex technology, selects a limited number of firms, thus determining concentration in market shares. Finally, the industrial dynamics are influenced by the evolution of the quality of the final good.

KEYWORDS

product innovation; product modularity; market dynamics; technological search strategy; agent-based simulations

1. INTRODUCTION

Innovation is largely recognised as a key determinant of industry dynamics in terms of both their composition and organisation (Malerba 2005). Indeed, technological competition among firms develops through patterns of differentiated dynamics related to the capacity of firms to cope with 'complex' technological problems and hence to obtain quite different performances in the market.

Within this perspective, in this paper we focus on the relationships between the dynamics of an industry, in terms, for instance, of firms' market shares and product quality, and the nature of firms' technological competition. More precisely, we concentrate on the role of product modularity in determining the effects of firms' technological research and, hence their competitiveness in production. In the innovation literature (e.g. Langlois 2002), product modularity is interpreted as the way in which changes in one component (or module) of a good affect the other components (or modules) used to produce the final good. Indeed, it is now widely accepted in the literature that product modularity affects the way in which firms 'de-compose' both their production and search activities. Problem decomposition is the way in which firms may simplify a complex problem (such as technological research) by solving each sub-problem separately (e.g. Simon 1969). Therefore, the level of product modularity determines the decomposability of production and technological complexity faced by firms that attempt to increase their relative share of the market.

To this and related literatures on industrial organisation, we make two contributions. We provide a preliminary explanation of the transformation of an industry as an outcome of the relation between technological complexity, product modularity and technological research. We employ qualitative simulation modelling, suggesting a theoretical framework and methodology that disentangles explanations of emerging complex behaviours and can be easily expanded. (1) That is, we describe firm behaviour by means of an agent-based model, and analyse the results firm search at industry level. The computational model allows us to provide an interpretation of the complex dynamics that result from combining product characteristics and firm strategies.

We model an economic system that represents one industry in which a set of firms produces a heterogeneous good. The good is characterised by a complex architecture, and is produced by assembling a set of intermediate components (modules). Before it is sold, the good is evaluated and selected by consumers on the basis of its characteristics (user services). The quality of the good produced, the market concentration, and the firms' fitness are emergent properties of the firms' search process in complex technological 'landscapes' for innovations in product modules (components). It is our contention that the degree of modularity of the production process is a crucial variable in yielding different outcomes in terms of market competition.

The paper is organised as follows. In Section 2, we sketch the theoretical background to the paper. Section 3 provides an abstract interpretation of the issues by describing the model in qualitative form. The simulation results are presented in Section 4 and Section 5 concludes.

2. THEORETICAL BACKGROUND

Market competition through technological change is at the core of neo-Schumpeterian and evolutionary economics analysis (Nelson and Winter 1982). Indeed, it is now common knowledge that firms in innovative sectors compete with rivals by searching for goods and processes of higher quality in an attempt to gain temporary monopolistic profits, rather than displacing competition based on cheaper output or production factors. The relation between technological change at firm level--with all its specificities in terms of radicalness, path dependency, lock-in, and the like, market structure, and some measure of global fitness, has permeated several research strands, with different degrees of closeness to Schumpeter's original work (Fagerberg 2003) and with different focal questions. Some of the research results have become well-established theoretical explanations and empirical evidence from firms in the analysis of industrial competition has had implications for market structure and market dynamics. We focus on those issues that the literature usually explains in terms of non-linearities and positive feed-backs in the competitive process, such as: 'first-mover advantages' (Lieberman and Montgomery 1988), 'persistent behaviour', 'path-dependence' and 'technological lock-in' (David 1985; Cowan 1990; Liebowitz and Margolis 1995).

We show that, given some myopia in firm behaviour combined with different degrees of product modularity, lock-in to inferior technologies (quality of product characteristics in our framework) may occur as the outcome of an over-evaluation of short-term fitness and imperfect understanding of the product architecture. With some interesting departures, we replicate some stylised facts of industrial competition that emerge when the 'complex' nature of technological competition is given a central role. Competing through product innovation is an inherently complex process, which does not allow a firm to hold all the information necessary to find the 'optimal' path. Bounded rational firms tackle this complexity by decomposing the problem (product innovation) into a set of 'independently-solvable' sub-problems. This is typical of the Simonian perspective (Simon 1969), which has implications in terms of industrial competition and dynamics that are at the core of a strand of recent research in evolutionary economics that focuses on the organisation of problem solving activities (Marengo et al. 2000), a strand on which we draw in this paper.

In the case of modular production this means that firms attempt to innovate in individual components of a complex good. This means that (depending on their starting conditions) firms often behave differently from one another and achieve a different fit with respect to market evaluation. The interaction between innovative, bounded rational firms with the complex market environment in which they operate, yields several interesting insights into the processes of industrial organization (Marengo and Dosi 2005).

The second strand of literature on which we draw deals with the degree of 'de-composability' of an innovated product, that is, the modularity of its technology (Langlois 2002) or as Ulrich (1995), Baldwin and Clark (2000), and Schilling (2000) put it, its product architecture. Indeed, innovation is more complex when the contributions of the individual components (e.g. intermediate commodities) to a product's integral fitness are highly correlated; in other words, when the architecture is more integral. This has been extensively argued, but mainly from industry level perspectives: the first one is based on the effects that architectural vs. modular innovations have on the competition between incumbents and new entrants (Anderson and Tushman 1990; Henderson and Clark 1990); the second focuses on the evolution of the market structure and the product architecture itself (Abernathy and Utterback 1978; Utterback 1994). Although we draw on this literature, we maintain a consistent microperspective, which is in line with the Simonian view of problem decomposition, and more aligned with a recent literature that analyses the limits and opportunities of technological modularity (Ernst 2005) in close relation to the organisational structure of firms (e.g. Brusoni and Prencipe 2001). In other words, the way in which firms tend to align the structure of innovation and product architecture.

By bridging these two perspectives, we hope to provide a significant contribution to the analysis of industrial dynamics--or at least of some aspects of it--by suggesting that it might emerge from the match between inherently uncertain firm technological research and the degree of modularity of the final product realised.

3. SIMULATION MODEL: STRUCTURE AND DYNAMICS

In this section we briefly describe the rationale, structure and dynamics of the simulation model used to address our research question. We present and discuss only its main features, and in a heuristic way, without getting into the technicalities, in order to focus on the elements that are essential for an intuitive interpretation of the results. The interested reader can refer to Ciarli et al. (2006) for a more detailed and technical description of the model's variables and algorithms.

Model structure: The economic system

We started by modelling an economic system populated by firms that produce a consumption good for a single market. The good is assigned a fixed number of characteristics, which represent the implicit use of the final consumers in a Lancasterian way (Lancaster 1966). Different firms may achieve different levels of quality for each characteristic. Consumers are thus confronted with a market that offers an array of heterogeneous goods, the distribution of which depends on the level of technological competition on the supply side. Consumers have preferences related to both price and use characteristics of the good, and are the main driver of the model's dynamics. Demand, in fact, increases monotonically with quality characteristics, depending on the preferences distribution, and decreases with respect to price. (2) To keep the model tractable, the demand side is aggregated, that is, it is composed of a set of homogenous consumers.

Each firm in this economic system produces a unit of the final good by assembling a given number of intermediate inputs. Each input is defined as a product component or module that is assembled in the produced good. The modules come with given levels of quality, and are technologically interrelated. That is, a change in the quality specification of one module (a product innovation, via the innovation of one component) alters the contribution (either positively or negatively) of the remaining ones to the assembled good being sold in the market. It follows then that the quality level of each user characteristic of the good depends both on the technological level of each product component, and, more crucially, on its modular/non-modular organisation. Finally, firms determine the price of the good as a mark-up on their variable costs.

The distribution of demand preferences determines firms' economic performance and, in turn, aggregate demand. The level of aggregate demand is in fact a function of the average quality level of the good's characteristics produced in each time period. The demand faced by individual firms (and hence production) is a fraction of total demand, and depends on technological competitiveness, and the level of quality of produced good's characteristics that is achieved.

As far as technological innovations are concerned, the economic system described above represents a production chain in which technological specialisation as well as the input-output structure are initially defined. We thus provide a reference model for those industries where components are inputs to the consumption good and contribute to its fitness (such as, for a example, a car or a computer). We also assume that firms in the consumer market can control the production process along the entire chain. In other words, although production occurs independently in each and every component sector, final tier firms manage the relative technological change along the entire chain. In other words, we model a vertically integrated industry. (3) This simplification allows us to concentrate on the innovation process of firms that may undertake both integral and modular research and do not depend on the suppliers' innovation strategy. (4)

Agent behaviour and model dynamics

The model variables evolve in discrete time. At the core of the dynamic structure of the model is that in each period, all firms in the market produce, innovate, interact and sell. At the beginning of each period, consumers observe and evaluate firms' output from the previous period, and determine the aggregate demand of the market, as well as the market share of each firm according to their quality performance.

After market transactions have taken place, firms attempt to innovate in order to increase their relative fitness and market share in the following period vis-a-vis their competitors.

Firms follow a three step route to innovation: (i) exploration of the technological landscape; (ii) evaluation of the new discovery; and (iii) potential adoption, which becomes actual adoption providing the innovation is successful.

(i) The exploration of the technological space simulates a sort of technological experimentation to find a better definition of one product component (e.g. a R&D lab), to be plugged into the assembled good. Firms are assumed to innovate on one single component per period. Each assembling firm thus randomly selects one module, and undergoes a search process, moving in any direction within the two-dimensional technological space of the single module. (5) We acknowledge that technological search is viable only in the cognitive space of the firm, and thus allows only for steps within the neighbourhood of the position previously reached. This yields a new value for the module. Given the correlation among modules (absence of full modularity) after technological change has occurred in one module, the firm finds itself in a new position of the N-dimensional technological space (where N-1 is the number of modules). And the change in the position may not reflect an improvement in the technology of the single module, if this has a negative effect on product fitness.

(ii) Once a new experimental component has been defined, the fitness of the prototype product is evaluated. We assume here the most general case in which firms have only partial information on the architecture of the produced good. This is similar to assuming that final tier firms do not know the modular relation between components, but can induce it from the combinatorial outcome of technological research. Accordingly, they evaluate the overall performance of the good with the new component. (6)

(iii) Eventually, the innovation is accepted if successful, and dropped if it is not. When the new component technology induces a better fitness, firms abandon the old technology and find themselves in a new position in the different dimensions of the landscape. When it does not, firms return to their initially known position.

The procedure described above makes use of a continuous approximation of the NK model, recently proved to be an algorithm well suited to describe search processes in a complex environment (Kauffman et al. 2000; Frenken et al. 1999). Using the terminology we have adopted for this paper, NK models can be used to represent a modularised search space, in which the degree of complexity depends on the extent of the influence between the N modules, measured by K, which represents the degree of interdependence between the modules and can range from 0 (total independence (7)) to N-1 (maximum interdependence). Because of their properties, NK models have been widely used, for example, to evaluate the performance of different search strategies under different degrees of problem complexity (value of K). Unfortunately, though theoretically feasible, their application to individual firms' strategic behaviour is computationally demanding. Therefore, we have adopted a mathematical system replicating the properties of NK models, but with a more flexible representation that can be easily plugged into larger models, which we will refer to as the Pseudo-NK (PNK) model (Valente 2006).

4. SIMULATION RESULTS: THE ROLE OF MODULARITY FOR INNOVATION AND INDUSTRIAL COMPETITION

In this section we briefly present and comment on the results obtained by simulating the model described above. We describe the initial configuration of the economic system and depict firms' innovation behaviour in a complex technological landscape, reporting its impact on their industry. Finally, we show how the level of modularity affects the evolution of the market.

In order to provide a clear understanding and interpretation of the results, and of the mechanisms through which they emerge, we assume firms to be quasi-homogenous: they differ only in the initial technological position of the modules on the landscape and in their productivity.

Simulation set-up

The model we analyse is a (fairly simplified) economic system characterised by a reduced set of entities (firms, characteristics of the final good and the relative modules). The model is initialised with the following characteristics. The economy is populated by 150 firms. Each firm produces a final good that is: (i) evaluated by consumers on the basis of two characteristics; and (ii) produced by assembling three not fully modular components (all correlated with each other, i.e. an integrated product).

As far as the characteristics of the final good are concerned, we first assume that the relationships among them are the same across the whole set of firms. Firms produce a good with the same product architecture, move in the same technological space, face the same technological complexity, and have the same decision strategy. With reference to the model this means that the direct quality contribution of an identical component on the characteristics of the good is the same across firms. Second, firms face the same technological frontier. Third, an identical innovation introduced in the same module affects the contribution of the correlated modules to the same extent.

Technological interdependence and emerging innovation strategies

Although we start with a set of quasi-homogeneous firms in a very simple setting, the complexity of the technological research, paired with the low degree of modularity, produces high heterogeneity in the results.

Figure 1(a) depicts the evolution of firms' market shares. During the initial time periods the advantage of first movers is clear; they start from a position on the technological landscape that allows them to comply with the technological complexity. Since the beginning of the simulated competition, these firms manage to introduce a sequence of successful innovations into the different modules (coherent with the product architecture). Thus, firms that are able early on to increase the quality level of the product characteristics gain rapid market shares (Fig. 1(b)).

However, as time goes by, a number of firms manage to find a path through the technological landscape, to innovate and to improve the fitness of the final good. As Figure 1(b) shows, several stable technological paths emerge, as different groups of firms achieve different levels of product innovation, from which they are unable to move further. It is interesting that only some of the firms that gained early market share end up on the highest paths. Some firms are not able to pursue the early successful innovations in the produced good, while some latecomer firms manage to reach the highest quality values (i.e. the global maximum) although it might take them longer (everything else being equal). (8) The dynamics of technological research are reflected in the long-run evolution of market shares (Fig. 1(a)). The largest shares are distributed among those firms that are able to understand the relationships between the modules' values over total fitness, i.e. that can successfully decompose the technological complexity of the product architecture into individual components. For those firms there is only one stable path: the highest one.

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The use of simulation allows us to investigate in depth the reasons why 'quasi-homogeneous' firms, with (the same) limited information on the technological landscape, shape heterogeneous market dynamics as an outcome of their innovation strategy. Figures 2 and 3 focus on the firms' innovation dynamics and depict two contrasting cases in which the dynamics of the technological search allow the firms to reach, respectively, a low and a high market share. Figures 2 and 3 show the changes through time in the value of each module (left axis--between 98 and 102) around the optimal value of the technological frontier (100), and the corresponding quality level reached by the product characteristics (right axis). It is important to mention that the model considers two different values for each module: (i) the actual 'position' values on the two-dimensional technological landscape; and (ii) the 'systemic' values that depend on the position on the landscape of the interrelated modules in the four-dimensional landscape. (9) When the two values coincide, the fitness contribution of a single module to overall fitness (quality of the product characteristic) is maximised. As an outcome of product nonmodularity, a very high value in the technological position of a single module may negatively affect the contribution of the other modules. (10)

The unsuccessful firm (Fig. 2) is able to increase the quality level of one characteristic quite rapidly, as the position of module 3 approaches its 'optimal' systemic value. However, in concentrating technological research on a single component (note that at the beginning, for this specific firm, the third module is the easiest to innovate), when it reaches its maximum level, innovations to the remaining two modules are rejected. The changes do not induce a sufficient increase in global fitness to counterbalance the loss of quality in module 3, which would have to depart from its optimal systemic value. Hence, the firm finds itself in a situation of technological lock-in, as soon as it reaches a local optimum. Indeed, to produce technological advances in the other modules (and thus increase global fitness) the firm would have to temporarily reduce its fitness. However, this does not happen as firms are characterised by bounded rationality and imperfect information.

Conversely, in Figure 3 we depict the case of a globally successful innovation path. The firm manages to reach a local maximum on a single component (module 1) only after a larger number of time periods, during which it moves along the different dimensions of the landscape. In doing so, the firm finds itself in a position where it can 'see' much farther in the landscape. Therefore, when it reaches the local optimal value for module 1, the systemic technological proximity with the remaining components (which means that the full modularity of the production process is taken into account) allows for a smooth tuning-up of the other modules in the following periods, thus avoiding being trapped into the local maximum. In particular, in temporarily reducing the systemic value of module 1, the firm manages to increase the value of modules 2 and 3, allowing it to climb further up the global fitness value. Only when modules 2 and 3 are firmly set on a fitness-increasing path does the firm refocus on the first module, and asymptotically approach the optimal technological level, given the product architecture. In this case, the successful firm can be described as pursuing an architectural strategy (i.e. involving the whole set of modules), while the unsuccessful firm would be pursuing a modular strategy (Anderson and Tushman 1990; Henderson and Clark 1990). The obvious trade-off for the different long-term fitness values is the opportunity to gain market share in the very initial periods. The strategy followed by the firm depicted in Figure 2 (the unsuccessful case), in fact, would be rewarded in an oligopolistic market in which the fixed costs are high enough to rule out firms with small market shares. This provides us with an interesting insight in terms of industrial policy and market failure: firms that produce a low quality good remain in the market. A correction of this failure can be pursued, increasing the dynamic efficiency of the market in terms of consumer welfare, by subsidising long-term research projects that explore the overall architecture of the product.

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Having shown how our model can explain quite standard results in the innovation/organisation literature, in the next section we use the model to analyse the functional relation between the level of product modularity, market structure and product quality.

Role of modularity

As shown above, a low degree of product modularity has a crucial impact on the final outcome of firms' technological search for product innovations. We now analyse the role of modularity on market structure evolution. In particular, we twist the degree of module interdependence between 0 (full modularity) and [+ or -]1 (full dependence of each component's technological contribution, either positive or negative, on the other components--integrated good, or absence of modularity). (11)

Here, the market is assumed to consist of 50 firms, each producing one good with two characteristics, comprised of six modules. Firms differ only in the initial position of each module on the technological landscape. For each simulation, all firms face the same product architecture: the technological complementarity is unique across firms and product characteristics. We ran simulations for 5,000 time periods and report average values for 10 simulation runs initialised with different random seeds (in order to avoid a bias in the result due to randomness).

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To start, Figure 4 depicts the relation between the value of modularity (a, along the vertical axis) and market concentration in the final period of the simulation runs. (12)

There are three particular interesting results. First, as expected, a decrease in modularity increases the complexity of the search for an optimal technology. Accordingly, when modularity decreases, a smaller number of firms is able to successfully innovate through time, and they end up with a larger share of the market. Consequently, the average quality of the final good sold in the market reduces as modularity decreases (see Fig. 6, below) at the same pace as the Herfindahl index increases.

Second, for a quite large interval of modularity 'values', the industry ends up in a condition of nearly perfect competition (each firm covers 2% of the market). Only when the technological interdependence between product components approaches its mean value does a large number of firms fail to innovate or to 'understand' the technological relation between components, which, in becoming more complex to manage, determine production concentration in few firms (Fig. 5 depicts the non linear increasing relation between modularity and market concentration).

Third, when we weight the value of modularity by the ratio of the positive correlations between modules (a proxy for their relevance), the relation between modularity and market concentration becomes less clear-cut (Fig. 4(b)). In fact, for the same level of market concentration, we observe both low and high levels of positive correlations among components (see, for example, between the 0.025 and the 0.03 values of the Herfindahl index) while negative correlations stick to the non-linear increasing relation depicted in Figure 4(a). This result is quite interesting, as it suggests that negative modularity has the strongest effect in hindering firms in finding the 'right' innovation path. When components are highly interrelated, providing the relation is positive, a quite high number of firms still achieve a good market share after 5,000 periods. If there is a negative relation among modules, simple trial-and-error innovation strategies that do not take account of the product correlation structure, are doomed to produce very poor results.

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The result for consumer welfare is similar to that for market concentration: the average quality level of the final good strongly reduces only when the interdependence among components reaches an intermediate level (Fig. 6(a)). (13) In practice, in order for firms to reach high values of global fitness, and for consumers to benefit from 'better quality' goods, products need not be completely modular, they need only be modular 'enough'. Above this threshold level, (approximately the mean level of interdependency between modules), the market becomes less open to competition, and a reduced number of firms achieves oligopolistic positions.

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Figures 6(a) shows that average quality levels across different simulation runs are highly clustered (low cross-simulation variance) for both very high and very low values of modularity, but are sparse (high cross simulation variance) in the intermediate range. Thus, for these intermediate values of modularity, firms' fitness largely depends on the random path of research undertaken at the beginning, rather than on deterministic variables. Indeed, when the architecture of a good is characterised by intermediate values of component correlation, the final outcome at firm and market levels is predictable only to a limited extent.

Finally, when the component correlation approaches the mean-threshold value, across-firm variance in the quality levels of product characteristics increases sharply, and stabilises again for high values of interdependencies (Fig. 6(b)). This S-shaped relation between modularity and quality variance confirms that: (i) with high modularity, many firms achieve the same optimal technology; (ii) with very low modularity, many firms are locked into low-level technologies, and few firms achieve optimal innovation; and (iii) between these two extremes, there is a region where small changes in the definition of product architecture have a strong impact on the future structure of the market, industrial dynamics, and quality of the marketed good. The result suggests that competing in a market of intermediate product modularity, strategic changes to the product architecture are likely to be cost effective. In fact, small changes to the architecture may yield large competitive gains, easing the outcome of technological innovation.

Previous results on the role of modularity in production are therefore confirmed by our model, which emphasises the role of modularity in easing the technological constraints faced by firms. (14) We now turn to the evolution of the relevant variables, that is, market structure and production quality, in order to better understand the causal linkages determining the results discussed above.

Market concentration

During the initial steps of the simulation, a strong market concentration occurs irrespective of the level of product modularity (Fig. 7(a)). This is due to the different timing in the innovation strategy across firms: initially, some firms manage to follow a path leading to one local optimum in the very short run, while other firms follow an integral strategy, innovating in the different modules alternately. By the time 'fast track' firms reach one optimum, the 'integral' firms are still far from optimum for any module (far from the technological frontier for every component). And the result is similar across the different values of technological modularity, as the capability to innovate in a single module does not depend on its relation with other modules. Over time, the initial advantages of the early innovators fades away, and late innovators approach the frontier in all the components. This allows them to erode market share of the early innovators and reduce the concentration of the market, until the long-term pattern is achieved. Here, the level of product modularity plays a significant role, as it determines which strategy wins in the long run. High modularity (up to an intermediate level) determines a near-to-perfect-competition market. For lower values, there are marked differences. Low modularity enables long-term high fitness following a wide range of different paths of technological search. Conversely, when modularity decreases, initial technological improvements on a single dimension hamper further innovation on the remaining dimension: initial winners are then outperformed.

Note also that the time to reach the long-term market structure differs for different modularity levels. In the case of low modularity, the initial technological lock-in of many firms leads to rapid oligopolistic competition among the technological incumbents; in the case of high modularity, it takes time for firms to compare the final outcomes of the different technological strategies: some simply take longer than others, but eventually reach very similar levels of fitness.

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Figure 7(b) depicts the cross-simulation variance of the Herfindahl index: in the cases of low modularity, the final value of market concentration is subject to stochastic elements. That is, the number of firms that achieve promising innovation paths differs substantially; and the final out come in the market ultimately depends on the competitive relations between firms, as well as on random elements.

Product quality

The evolution of market shares distribution is determined by changes in the quality of the good's characteristics. Indeed, the average output quality achieved by firms is higher, the higher is the modularity, i.e. when the search in the technological space is easier. Figure 8(a) presents the simulation results for cross-firm average values for first quality characteristics for different modularity values. (15) Irrespective of the level of modularity, on average, firms initially are able to innovate to very similar extents. However, the drawbacks of technological lock-in increase through time more than the reduction in product modularity. The large differences in cross-firm variance clearly show how firm performance in the market diverges as the complexity of technological research increases (Fig. 8(b)). It is important to note that a large array of low modularity values affects the variance in the quality of the good produced by competitors in the same way (when the strength of correlation between modules is above 0.75). This result confirms the above discussion on the evidence depicted in Figure 6(b): above a given level of product 'complexity', there is little difference in the segmentation of the technological achievements of firms resulting from research. Few firms are able to disclose the technological features of the product they produce, and thus substantially increase the final value of their product, while most of them stick to a low level of production quality granted by the 'simple' initial innovation.

Nonetheless, even in the most complex scenario, at least one firm manages to produce a good with the highest possible quality level, using frontier technology. In fact, there is almost no difference across simulations in the maximum quality value achieved, independent of stochastic events and the level of modularity (Fig. 9). Figure 9 shows that, in the case of low modularity, firms need a much longer time to reach the technological frontier (the variance in Fig. 9(b) goes to zero only after a large number of periods). Therefore, what changes across simulations (due to stochastic determinants) is the number of firms that are able to achieve this maximum level of product quality.

5. CONCLUSIONS

In this paper we proposed a simulation model to analyse how product modularity affects the outcome of firms' innovation activity, their ability to gain market share, and the resultant market structure. The model was first employed to explain the mechanisms behind standard results on firms dealing with complex technological landscape. We then analysed the effect of this complexity on market dynamics and the quality of the goods sold in the market.

Analysis of the simulation results allows us to draw some preliminary conclusions and policy implications, at the level of the firm, the industry in which they operate, and the overall market. First, we show that, due to limited modularity, firms that start from very similar technological conditions end up in very different positions in the market. Different initial perceptions of the product technologies, and limited information on the way in which the different technologies are integrated with final product fitness, induce a number of research strategies, quite heterogeneous across firms in an industry. This provides an explanation of the evolutionary process induced by the interplay of variety generation and selection as a result of product innovations in complex technologies, rather than random changes in the efficiency of production processes.

Second, we show that the trade off between modular and integral technological search is extremely relevant in conditions of low modularity. On the one side, focusing on innovations in a single module over a long period, increases short-term competitiveness, but may lead to technological lock-in. On the other side, focusing on understanding a complex architecture may require too long a time, in a highly competitive market, but may lead to the highest quality level. This suggests that an architectural innovation is not always preferable to a modular one: it depends on the level of modularity.

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Therefore, in the presence of low modularity, some kind of incentive would allow firms with long term strategies to stay in the market, and benefit consumers. In other words, market mechanisms could easily fail to provide an optimal outcome from the consumer's point of view. Nonetheless, we have shown that full modularity is not required, if the objective is to promote a competitive market in which most firms can find their way to an optimal innovation strategy.

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Third, our analysis suggests that the opportunity for firms to act on the architecture of the product, and thus increase modularity to an intermediate level, is sufficient to easily decompose innovation and production into modules. Therefore, architectural search, combined with product innovation, is a reasonable strategy for given levels of low modularity. However, it should be noted that, based on our results, intermediate modularity means that firms' innovation outcomes are highly dependent on random changes in the innovation process. Eventually, the need to control an integral architecture, versus the need to reduce complexity into sub-problems, directs attention to the firm's vertical strategy. Future work is required to understand how changes in product modularity affect firms' organisational strategy and also the market structure.

In terms of the market, we show that product modularity plays a role in determining market concentration as an outcome of the firms' capabilities to compete. From an industrial policy perspective, this should be taken into account when evaluating oligopolistic situations. Indeed, 'quasi-natural' monopolies may arise, not because of high fixed production costs, but rather because of the low level of modularity, which requires huge innovative efforts along a wide range of technological dimensions. This is relevant in markets where the quality of the good/service is an important policy issue (e.g. transport equipment, health services, products with major environmental impact).

Finally, one should take into account that a high level of market concentration can also occur because firms that under-invest in the architecture during the initial stages of the competitive process, provide the market with an output which is sufficiently good with respect to some of its components. As our analysis shows, ruling out firms that invest in the architecture in the initial stages, may induce technological lock-in for the whole market, which should be considered when designing innovation policies not exclusively aimed at fostering firm growth.

Acknowledgements

Previous versions of this paper were presented to several workshops of the PRIN Project 'Dynamic Capabilities between Firm Organisation and Local Systems of Production', and to the DRUID Summer Conference 'Knowledge Innovation and Competitiveness: Dynamics of Firms, Networks, Regions and Institutions', Copenhagen, June 18-20 2006. The authors are indebted to all the participants, and in particular to Stefano Brusoni, Bo Carlsson, Giovanni Filatrella, Thorbjorn Knudsen, Mauro Lombardi and Alessandro Lomi for useful comments and suggestions. Two anonymous referees have allowed to improve the paper substantially. Usual disclaimer applies.

Received 24 October 2006 Accepted 3 October 2007

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TOMMASO CIARLI

CIBI

Manchester Metropolitan University, UK and Department of Economics

Systems and Institutions

University of L'Aquila, Italy

RICCARDO LEONCINI

Department of Economics

University of Bologna, Italy

SANDRO MONTRESOR

Department of Economics

University of Bologna, Italy

MARCO VALENTE

Department of Economics

Systems and Institutions

University of L'Aquila, Italy

Endnotes

(1) See, for example, Ciarli et al. (2008) for a first extension.

(2) Price may thus be conceived as a further characteristic of the good with negative impact on utility.

(3) In a different paper, we analyse the relation between technological modularity and industrial organisation (Ciarli et al. 2008).

(4) This assumption is necessary to analyse thoroughly the role of modularity on market composition. Indeed, if the fitness of firms in the consumer market depends also on the technological behaviour of their suppliers, we would not be able to isolate the effect of modularity. This problem is tackled in Ciarli et al. (2008).

(5) As explained more fully below, the two dimensions refer to the value of the module and the step in time taken during each exploration.

(6) A fully informed firm would evaluate innovation on one module with respect to its correlation with the remaining product components (reducing the complexity of the environment).

(7) If there is no interdependence among the modules, then the solution of the problem is 'straightforward', and needs no specific strategy. In fact, the solvers' strategy can be applied in parallel to all the modules to obtain the highest fitness solution to the problem in a relatively small number of steps.

(8) The fact that different starting conditions allows for a relatively easier and faster search of the technological landscape is highly relevant when one includes entry-exit dynamics, which here are ruled out for the sake of simplicity.

(9) The fitness value depends also on the product architecture, i.e. on the strength and sign of the relations between modules. For a complete description of the model and a full understanding of its dynamics, refer to Ciarli et al. (2006).

(10) As a straightforward example you could think of inserting a very powerful Formula one racing car engine (highly technological in its own domain) in a small city car. The car would be very fast, but also outstandingly unsafe. And the two quality characteristics would clash.

(11) In this analysis we assume that, unless components are completely independent from one another (full modularity), all components are interrelated.

(12) An increase of a, in absolute terms, means a decrease in modularity. In Figure 4 we report both positive and negative values of a, as we take into account both positive relations between the fitness of two modules (an improvement in one module improves the fitness of another) and negative relations (an increase in the fitness of one module induces a decrease in the fitness of another).

(13) Figure 6a depicts the second product characteristic and for the average negative value of a as an example, all other combinations being very similar. Other results are available from the authors.

(14) As we show in another paper (Ciarli et al. 2008), the relevance of modularity also depends on other variables related, for instance, to the product life-cycle--modularity can exert advantages once a standard to produce the final output is agreed upon by a sufficiently large set of firms in one industry--or to the distance of the firm from the technological frontier--as the distance increases, a more integrated production process might be required in order to better evaluate architectural innovations and benefit from them.

(15) The results for the second characteristic (not shown) follow the same pattern.