Roles, Artefactos y Reuniones de Scrum

6 3.2.1.1. The “Both Firms Innovate” Term

The relevant term to be maximised by jointly choosing the values of a, 6, 0^^

and is +

Computing the first derivative of the expression above with respect to 6^ will

give- I

a/?, ^

A similar expression may be found by computing the first derivative of the same term with respect to Oj^. Recalling our previous knowledge of the partial derivatives involved in the expression above, we can observe that the first two terms on the right hand side are negative whereas the last two are positive. One might be tempted at this point to say that and then invoke the domination of the direct effect over the indirect effect to conclude that the whole derivative is negative and thus the optimal value of 6^ (and similarly 9j^) would be 0. Notice however that, by coordinating the R&D activity, firms may find profitable for just one firm to share the knowledge, and so we would have 6^ different from . This is not an affirmation that firms have any type of incentives to follow such strategy, but is one possibility available to them. If this is the case, then it would no longer be true that

which makes it impossible to say whether the direct effect dominates the indirect effect or not. Given this fact, the analytical study of this situation becomes more complex and we need to resort to alternative methods of obtaining the results.

As there are four endogenous variables involved, the use of graphical analysis is unrealisable. We are then left with numerical simulation methods. Noticing that firms have to jointly decide the values of a, h, 0^ and 9j^, the solution for both stages of the game can be (and probably will be) found simultaneously. So, the program written to numerically simulate the results, tries to capture the combination of values of a, b,9^ and 9j^ that maximises the profit level. Obviously, it would be unfeasible to simulate all the possible values for each variable within the interval [0,1], and for that reason the program analysed all the possible combinations of those variables considering they assume values to the second decimal case (i.e. increments of 0.01). The output of the numerical simulation may be summarised by the following table, which just displays the results of the possible combinations when the variables in question assume the extreme values^:

^ Several values of g were considered in the simulation, however this variable does not seem to be relevant for the choice of the decision variables, as it was not in similar circumstances with different assumptions about spillovers.

Ô Ù g = 0,1 .93339132 .93339132 .92579568 +##4456 .93505972 .93162627 .92131309 .93162627 .93505972 .92131309 +##4456 .93339132 .93339132 .91638963 #31206$ .93339132 .93339132 .88889022 .m tm È .93956337 .92564878 .83177472 #312068 .92564878 .93956337 .83177472 .95512068 .93339132 .93339132 .71221361

Table 6.1. Joint profit level for different values of a, b, 0^ and 0^^

From the observation of table 6.1 it is straightforward to conclude that the variable values in the shadowed cells are those that maximise the joint profit level, whatever the value of g considered. In spite of the fact that the value of this variable might be relevant for the profit level itself, it has no impact in the choice of the decision variables.

Not only by closely checking the complete output of the numerical simulation but also by looking at the values involved, it becomes obvious that the relevant decision in such a setup is the choice of the research design. With respect to this stage, the results show that the optimal value for a and h is zero, which creates from the beginning a situation of maximum product differentiation. As such, and given the hypothesis of the model, there will be no chance for the creation spillovers (adaptability is non-existent). Therefore the choice of the level of information sharing is irrelevant. This explains why in the table summarising the results we get the same

profit level for of a = 6 = 0, irrespective of the values of 9j^ and 6^^. The decision at the research design stage pre-empts the information sharing stage.

This type of result cannot be considered a novelty if we take into account the conclusions and explanations of previous chapters when analysing a similar context. Notice however that, with the introduction of the new mechanism for spillover control, we can conclude that in spite of the benefits spillovers may cause to the firm that receives it (and that makes this firm willing for its to rival share all the information), these are not enough to compensate the loss in profit the firm generating those spillovers would have if information was shared^. So, in aggregate terms, it is not profitable to share information, despite the fact that individually each firm would profit if its rival allowed the spillover to occur.

6.3.2.I.2. The Only Firm L Innovates” Term

In this case firms will be interested in maximising +

and have to jointly decide the values of a, b and in conformity with such an objective. As firm R will not innovate, firms do not need to decide on the optimal level of information this firm will share, as it will not generate any. From what was learned when the certainty case was analysed, it is not surprising that the achievement of conclusions using exclusively analytical methods will not be feasible. This can be easily seen in the expression of the first derivative of the joint profit expression with respect to 0^ -.

Ô0C,

da^

00^

da^ d0^

d0^

The first two terms of the expression are negative and the last two are positive. This depicts the opposite incentives firms have concerning the level of information sharing; the innovating firm prefers not to share any information whereas the non­ innovating firm would benefit from the spillovers. As we cannot clearly conclude which effect dominates from the profit expression and respective derivative, an

^ Losses would be caused by decrease in the specialisation characteristic quality gap and/or the increase of the rival’s advantage in its specialisation characteristic.

alternative method of analysis will be utilised. Numerical simulations were run and graphical analysis will also be used. As both methods provide the same results, the optimal values for the endogenous variables reached in the numerical simulation will be mentioned and re-enforced with some of the plots of the graphical analysis, which are perhaps more revealing and appealing.

The program used to run the numerical simulation was similar to the one utilised in the previous section: it finds the values for the combination of variables a, b and 0^ that maximises the joint profit. This was done considering the usual value of S= 20, and = 0.1, 0.2, 0.3, 0.4, 0.5. The output of the numerical simulation pointed to the fact that, whatever the value of g considered, the optimal combination of variables was: a = 0, b = 0.26, 6^ =

Before analysing these results it is also useful to look at some plots of the joint profit level: 0 . 9 3 6 0 . 9 3 4 P r o f i t 0 . 9 3 2 0 . 9 3 0 0 . 2