The analysis undertook in the previous section was made considering the situation where firm L was the only firm to innovate, however, given the way the model was setup it is easily observable that firms’ identity are once again irrelevant and the conclusions obtained in the previous section can be generally applied to the case where there is only one irmovator. Obviously, the results concerning firm L are applied to the innovating firm, and the choices of firm R are in respect to the decisions of the non-innovating firm, irrespective of their identity.
6.3.2.2. Uncertainty Case
As it is usual in this case, firms will have no information on the outcome of the R&D activity and as such will have to take into account simultaneously all the scenarios they may find themselves in after the R&D uncertainty is resolved. Contemplating this, they will have to choose the values of a, b, 6^ and that maximise the following expected joint profit expression:
/’H - W K ('«K. A >* +
X*]+n -
^ J +
^ j ]
As it is probably evident by now, a complete analytical analysis of the above expression will not be feasible, forcing the use of alternative methods in order to achieve results. Given the number of endogenous variables involved, the utilisation of
However, even if it is the case that the latter are dominated by the former, the results point to the fact that these are also dominated by the consequences of the alteration of gap magnitude in the profit of the firm that is specialised in that characteristic. This points to the idea that firms’ profits are more sensitive to the own specialisation gap than to changes in the rival’s specialisation gap.
graphical analysis does not constitute an alternative, as we are limited to three dimensions. Therefore numerical simulation will be used.
The aim is to find the combination of values of those four endogenous variables that achieve the highest profit level possible. As firms coordinate their choices in this respect, the result will certainly be the strategy chosen by firms.
Given that a complete presentation of the output would probably be tiresome and tedious the results that will be displayed concern all the possible combinations of variable values, only admitting that these assume extreme values. Notice however that the simulation was run considering that each variable could assume any value within the interval [0,1] up to two decimal cases, but no valuable insights were gained.
The usual value of S=20 was considered. The values of the remaining parameters were chosen by their representativity of other values they might assume.
g = 0.1 p = 0 ,I g = 0,4 p = 0 ,l g = 0,1 p = 0,9 a b ^ L ^ L ^R ;r^+;r^ 0 Ô Ô : G Î 7956527 10467551 1 0 0 0 1.7730945 1.7674834 1.0266917 1.0260682 0 1 0 0 1.7730945 1.7674834 1.0266917 1.0260682 1 1 0 0 1.7661387 1.7368569 1.0191671 .98310874 Ô Î g g u m u l Î 7956527 \ : Î 0467531 1 0 1 0 1.7749454 1.7772006 1.0283804 1.0326342 0 1 1 0 1.7714959 1.7621559 1.0249451 1.0185940 1 1 1 0 1.7621270 1.7071626 1.0147369 .92904004 0 Ô 1 h i m m 17956527 i m m i 2.0467531 1 0 0 1 1.7714959 1.7621559 1.0249451 1.0185940 0 1 0 1 1.7749454 1.7772006 1.0283804 1.0326342 1 1 0 1 1.7621270 1.7071626 1.0147369 .92904004 0 Û Î 1 m m 6 i 17956527 ;: i ^ n m u ; 2.0467531 1 0 1 1 1.7733565 1.7720301 1.0267208 1.0265734 0 1 1 1 1.7733565 1.7720301 1.0267208 1.0265734 1 1 1 1 1.7580712 1.6712238 1.0099098 .81877029
Table 6.2. Joint profit level for different values of a, b, 9^ and 9^^, considering different pairs of (g, p)
As was the case when the cooperative equilibrium was studied in a context where both firms were sure that they would innovate, now the conclusions that we obtain from the observation of the table above are similar. The basic result is that, when firms cooperate and there is uncertainty involved about the R&D outcome, the best strategy to follow is, at the research design stage, to choose to produce products as differentiated as possible. A natural consequence of such a strategy is, given the way the model was setup, that no spillovers will exist as firms capacity to adapt the knowledge flowing from the rival firm is null. Thus any decision concerning the level of information to be shared on the second stage of the game is totally irrelevant, since there is no useful information to be shared. This can be easily seen in the tables above as the highest profit level is reached whenever a = b = 0, whatever the values of 6^ and . Once again, the choice made in the first stage of the game pre-empted the second stage of the game.
The conclusion above is not surprising if we recall the results obtained when firms cooperated but the second instrument for spillover control was not available - chapter 5. With regards to the cooperative equilibrium, if we compare the present with the preceding chapter we can conclude from the term-by-term analysis that either this second instrument is irrelevant or it serves the purpose of guaranteeing that all information is shared, as in the fifth chapter. This points to the fact that the coordination of research design is sufficient for firms to maximise the profit level, not being necessary the introduction of a new instrument that facilitates the reduction of information sharing.
Notice that the result obtained does not mean that firms will be automatically willing to share all the information just because they are coordinating research design. In fact, the decision of adaptability (research design choice) implicitly conveys the idea that firms want to avoid spillovers, however in order to do so they do not need to resort to a second instrument of spillover control. This result corroborates to some extent the results obtained by Katsoulacos and Ulph (97) which conclude, in a different framework, that a cooperative agreement in R&D does not imply full information sharing.
Before concluding this chapter it is perhaps worthwhile to make a brief comment on the assumption utilised throughout the present chapter that firms could totally control the level of spillovers they pass to rival firms. It was noted, when the changes to the model were introduced, that in spite of in practice there may exist a limit to the extend firms control the spillovers, this would not be taken into consideration in order to keep the analysis simple. One might ask now, in the presence of the results obtained and in light of the conclusions of previous chapters, what consequences could have the consideration that there is a minimum amount of involuntary spillovers, which firms cannot avoid*.
The possible changes to the results reached in this chapter can be easily grasped and may be grouped in two types:
1. The cases where the research design choice implied maximum product differentiation and therefore those variables (a and b) were set to zero, and the cases where, in spite of a or 6 being strictly positive, the level of information firms are willing to spillover was set to its maximum (0 = 1). 2. The cases where a or/and b were strictly positive (choice of lower product
differentiation at the research design stage) and firms chose not to allow any spillovers by setting 8 = 0.
When the results obtained in a particular situation fall in the first category, it is fairly easy to observe that the imposition of a lower limit to spillover existence is innocuous. This stems from the fact that either the choice at the research design stage was one of maximum product differentiation thus pre-eliminating any spillover possibility (the value of 0 becomes irrelevant as there is no information to be shared), or it is in the firms best interest for knowledge transference to be at its maximum level ( 0 = 1 ) and for that reason any lower bound for involuntary spillovers does not constitute a constraint.
If however the results obtained are of the second type, then a little more attention has to be put into the analysis. By setting 0 to zero and then choosing a research design that would generate spillovers, firms are making use of the power they
have to exogenously control spillovers in order to adopt a strategy of less product differentiation while avoiding the impact this would have on knowledge transference. This was the case of the non-cooperative situations analysed where firms were (potentially) asymmetric^. In these contexts the spillover control instrument plays an important role as can be inferred by comparing the results obtained in the relevant sections of this chapter with those of chapter 5, where firms were bound to transfer all “adaptable” information/knowledge. Given this we should expect the conclusions to change if a strictly positive lower limit to 0 is to be considered. Notice however that, if such assumption is made, the results obtained both in chapter 5 and in chapter 4 make the alterations to the conclusions of the present chapter^® somewhat predictable.
The analysis of the changes in the results in a non-cooperative setup in case only one firm innovates can be enlightening. When firms have no ex-post control over the information that is passed to the rival (as in the previous chapter), the innovating firm will choose to differentiate its product as much as possible and its rival will try to minimise product differentiation in search for spillovers. However, if spillovers are non-existent (because 0 will be set to 0), the innovating firm might want to produce less differentiated products, whereas the research design of the non-innovating firm becomes irrelevant. Thus we may conclude that the consideration of spillovers discourages a firm that was successful in the R&D activity to differentiate its product less, as it would be giving away more spillovers. Such a conclusion is also supported by the results obtained in the fourth chapter where different spillover magnitudes were considered to exist, although in a different framework. Given this we can deduce that as the level of involuntary spillovers increases (as it would if a lower bound to 0 was considered) the innovating firm will be more willing to differentiate products more in order to increase the appropriability of its discovery, and the non-innovating firm will try to capture the spillovers by differentiating less. So, there must exist a threshold value for the lower limit of 0 for which the decision of the innovating firm concerning product differentiation is reversed.
^ This would imply that the lower limit of 6 is no longer 0, but a strictly positive value, possibly exogenously given.
^ The cases where only one firm innovates for sure or the outcome of the R&D activity is uncertain and thus might generate an asymmetric situation.
Keeping in mind that it is the situation of firm asymmetry that explains the strictly positive values obtained when uncertainty about the R&D activity is considered, the differences in the results that would be obtained for the uncertainty case if a lower bound to 0 was assumed, follow a reasoning similar to the one just explained.
6.4. Conclusion
This chapter studies the effects on the decision of product differentiation of the introduction of a mechanism that allows firms to control the amount of information they are willing to share (in case they make a discovery). It also analyses how this new mechanism will be utilised by firms. Therefore there will be two distinct phases in which firms will be called to decide. The first is at the research design stage, which happens before the R&D activity takes place, and where firms have to decide how they would like to improve their products - this will determine their capacity of spillover absorption^\ The second stage occurs when R&D uncertainty is resolved and the innovating firms have to choose the amount of information to share with the rival. So, the novelty in this sixth chapter is the consideration of a new stage that also affects spillover magnitude but that is not directly linked with the choice of research design - this was inspired by Beath, Poyago-Theotoky and Ulph (97) and Katsoulacos and Ulph (97), when these authors describe the nature and source of spillovers.
In order to gradually increase the model’s reality adherence, this new feature is studied cumulatively with many others introduced and analysed in preceding chapters.
The results obtained can be grouped into two types, depending on whether we are considering a non-cooperative or a cooperative setup. With respect to the former, we can conclude that in case both firms are sure to innovate the introduction of a mechanism of spillover control becomes irrelevant as firms prefer to maintain their decision of maximising product differentiation at the research design stage. This option obviously pre-empts the second stage of the game as spillovers will not exist and thus
This stage has been the object of analysis of preceding chapters.
there is no “adaptable” information to be shared. So, the choice of the information sharing level is irrelevant. If this new instrument is useless in a situation where firms know beforehand that their symmetry will be kept, this is not the case when firms know that an asymmetric outcome will arise from the R&D activity. In such circumstances it is somewhat intuitive that the innovating firm (the only one that has the power to decide how much information to share) will neutralise spillovers by choosing not to share any information. The rationale behind this is that if the innovating firm chose to share some information it would only be truncating its own gap advantage whilst allowing its rival to increase its ovm gap. Thus, it would be giving away something without receiving anything in exchange. Notice however, as a curiosity, that the non-innovating firm has the opposite incentive, i.e., it would like the innovating firm to share all the information as this is the only way it has to improve its product and not be left so behind its rival.
Keeping in mind the results obtained in a certainty context it is evident that in an uncertainty context, firms’ decisions will not change: firms will always choose not to share information as information sharing brings no advantages to the innovating firm and can in fact be harmful. Given this type of solution for the second stage of the game, firms are aware that spillovers are out of the picture. As such, their behaviour concerning research design choice will follow exactly the conclusions obtained in the third chapter where it was assumed total spillover absence.
When it comes to the study of the cooperative setup it can be considered that the second instrument of spillover control introduced in this chapter is useless. When we compare the results obtained with those of the previous chapter, where information sharing was exogenously set to its maximum, we observe that the same type of results is achieved. This is due basically to two facts: either firms choose a research design that automatically rules out spillover existence (certainty context/ both firms are sure to innovate; uncertainty context) which makes the second stage irrelevant, or the level of information sharing will be freely set by firms to its maximum, which mimics the circumstances of chapter 5, implying the same results for the research design stage. Therefore, we may conclude that in a cooperative context, the permission given to firms to control for the level of information sharing (as opposed to a situation of forced full information sharing) is redundant, as firms by coordinating the relevant aspects of
R&D activity will freely choose to share all the information and achieve the same profit levels. This occurs as cooperation implies the commitment the firms have in maximising joint profit and abiding by the strategy chosen to do it. For this reason, firms do not need to reduce the level of information sharing as what is spillovered can be perfectly controlled through the research design choice. In particular this means that, for instance, in spite of the fact of not being profitable enough to allow a great spillover magnitude, this can be set to its optimum size just by correctly deciding the research design that will cause such desirable spillovers to occur and simultaneously allowing them to be totally transferred.