Innovation and competition in complex environments.

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.