Innovation and competition in complex environments.

(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.