Innovation and competition in complex environments.

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).