Innovation and competition in complex environments.

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.

[FIGURE 5 OMITTED]

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.

[FIGURE 6 OMITTED]

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.

[FIGURE 7 OMITTED]

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.