394 M.P. Gos´albez, J.S. D´ıez J. of Economic Behavior Org. 42 2000 385–404
because, in a separating equilibrium, firm 1 always discloses the subsidy and consequently, not to receive the information signals firm 1 as a subsidized firm.
6. The case of strategic substitutes: a numerical simulation
When the efforts exerted by the firms are strategic substitutes, an increase decrease in firm i’s effort is best responded with a decrease increase in firm j ’s effort implying
negatively sloped reaction functions. We are going to use the following probability function: P e
1
, e
2
= e
1
+ e
2
− e
1
e
2
. 6.1
This function could represent a situation in which the partners have similar research abilities, each firm undertaking the whole project in its own laboratory, and they ex ante agree to
share the innovation no matter which firm innovates first. As Morasch 1995 explains, this kind of cooperative agreement is formed because, even if the synergy effects are negligible,
they reduce the risk of failure relative to the case of individual RD.
7
Given the complexity of the explicit expressions of efforts and transfer payments, we provide a numerical simulation to illustrate this case. The intuitions behind the results of
the simulation are, however, simple. If firm 1 discloses the subsidy firm 2, anticipating a higher effort from its partner, will react by exerting a lower effort, which hurts firm 1.
Therefore, we can expect in equilibrium
e
∗R 2
e
∗N 2
and e
∗R 1
e
∗SN 1
e
∗NN 1
. Figs. 2 and 3 display the results of the numerical simulation. In Fig. 2, the equilibrium
efforts of both firms are represented in the e, s space for three different subsidies s = 0.2, 0.3, 0.4. Those efforts have been calculated for λ = 12, V = 0.5 and for a conditional
probability ˜ q =
12. As can be seen, our expectations are satisfied by the simulation.
8
In Fig. 3, we have represented in the λ, s space the λ values delimiting the regions of separating and pooling equilibria, for three different values of s, for V = 0.5 and q = 0.5
and for the cases of strategic substitutes and complements. In order to do that, we have compared firm 1’s actual expected profits in the cases of disclosure and non-disclosure
when firm 2 has beliefs either t = 1 and ˜ q =
0 or t = 0 and ˜ q = q,
for the cases of separating and pooling equilibria, respectively. Regarding notation, λ
S
SC stands for ‘separating’ and ‘strategic complements’, while λ
P
SS stands for ‘pooling’ and ‘strategic
7
In our setting, cooperative RD is preferred by the firms to the alternative of individual RD, simply because cooperation reduces the probability of failure we need just to compare the probability of success in both cases,
that is, e
i
and e
i
+ e
j
− e
i
e
j
. However, if the innovation is to be shared between the partners for example, because they compete in the innovation market, and in order to guarantee that both firms prefer the cooperative option,
we would also need to assume the existence of a positive fixed cost incurred to start the project, that the firms can share through cooperation.
8
We have repeated the simulation for different values of V but the qualitative results do not change. We have also calculated the transfer payment, and it is always positive for this value of λ, implying that it is firm 2 who
pays it to firm 1. On the other hand, the transfer payment is always higher when firm 1 discloses the subsidy than when it hides that information. Therefore, from the transfer point of view and for λ = 12, disclosure is always
profitable for firm 1. The results of the simulation on transfers are available from the authors upon request.
M.P. Gos´albez, J.S. D´ıez J. of Economic Behavior Org. 42 2000 385–404 395
Fig. 2. Equilibrium efforts.
Fig. 3. Separating and pooling equilibria.
396 M.P. Gos´albez, J.S. D´ıez J. of Economic Behavior Org. 42 2000 385–404
substitutes’. As we already know, with strategic substitutes, if firm 1 discloses the subsidy, firm 2 reacts by decreasing effort, which hurts firm 1. This effect should obviously reduce the
region of separating equilibria, relative to the strategic complements case. Fig. 3 confirms our intuitions.
9
On the other hand, observe that as the subsidy increases, the interval of separating equilibria is enlarged and the interval of pooling equilibria is reduced. Finally,
notice that for λ values lying between each pair λ
S
, λ
P
for a given subsidy s, both a pooling and a separating equilibria simultaneously exist.
7. Should the subsidization of RJVs be made public knowledge?
