392 M.P. Gos´albez, J.S. D´ıez J. of Economic Behavior Org. 42 2000 385–404
it is firm 1 that pays the transfer and this fact provides firm 1 with incentives not to disclose the subsidy in order to pay a lower transfer. On the other hand, for high values of λ, it is firm
2 that pays the transfer and, therefore, it is in the interest of firm 1 to disclose the subsidy in order to receive a higher payment from firm 2. If the efforts are strategic complements and
firm 1 has disclosed the subsidy, by direct substitution of the equilibrium efforts in 15 we obtain
T
R
= 2V
3
31 − s [2λ − 1].
4.2 On the other hand, if firm 1 has not disclosed the subsidy, the size of the transfer will
depend, among other things, on the conditional probability ˜ q
. In this case, direct substitution of the equilibrium values in 15 results in
T
N
= 2V
3
3 1 − ˜
q + ˜
q 1 − s
12 2
[2λ − 1]. 4.3
Notice that the transfer payments increase with both the subsidy and with the patent value. Moreover, for values of λ lower than 12,T
R
and T
N
become negative, implying that it is firm 1 that pays the subsidy in both cases. Finally, comparing both transfers we obtain
that T
R
− T
N
T 0 if λ T 1
2 ,
that is, from the point of view of the transfer stage and with strategic complements firm 1 has an incentive to disclose the subsidy only for high enough values of λ.
In the following section, we will analyze firm 1’s optimal decision on whether or not to disclose the subsidy to its partner. In order to take this decision, the firm will take into
account its effect on the transfer payment as well as on the equilibrium efforts.
5. The disclosure decision
If firm 1 receives a subsidy s from its government, it has to decide whether or not to disclose that information to firm 2. In order to do that, it compares its actual expected
profits if it discloses the subsidy, E ¯ 5
R 1
, and if does not, E ¯ 5
SN 1
. Those profits depend on the strategic relationship between efforts and on the effect that disclosing has on the transfer.
We will analyze the existence of pooling, separating and semiseparating equilibria.
5
In a separating equilibrium, firm 2 believes that firm 1 prefers to disclose the subsidy and firm 1, given such beliefs, chooses to disclose the subsidy. Therefore, in a separating
equilibrium it is satisfied n
t = 1, E ¯
5
R 1
≥ E ¯ 5
SN 1
o .
5
We use that nomenclature from Funderberg and Tirole 1991.
M.P. Gos´albez, J.S. D´ıez J. of Economic Behavior Org. 42 2000 385–404 393
In a pooling equilibrium, firm 2 believes that firm 1 prefers not to disclose the subsidy and firm 1, given such beliefs, chooses not to disclose the subsidy. Therefore, in a pooling
equilibrium it is satisfied
n t =
0, E ¯ 5
R 1
≤ E ¯ 5
SN 1
o .
This is the most interesting equilibrium, as it provides a theoretical explanation for the empirical observation that motivates this work, that is, the lack of information regarding the
existence of subsidized partners that some firms participating in Eureka projects report. Finally, in a semiseparating equilibrium, firm 2 believes that firm 1 will disclose the
subsidy with a probability t ∈ 0, 1 and firm 1, given such beliefs, is indifferent between disclosing the subsidy or not. Therefore, in a semiseparating equilibrium it is satisfied
n t ∈
0, 1, E ¯ 5
R 1
= E ¯ 5
SN 1
o .
Next proposition displays the different equilibria in the disclosure stage for the case of strategic complements.
Proposition 5.1. If the efforts are strategic complements, there exist two real numbers λ
S
and λ
P
, with λ
S
≤ λ
P
, such that there exist a separating equilibrium ∀λ ≥ λ
S
, a pooling
equilibrium ∀λ ≤ λ
P
and a semiseparating equilibrium ∀λ ∈ [λ
S
, λ
P
], where λ
S
and λ
P
are given by λ
S
= 1 − s
12
1 − 1 − s
12
2s ,
λ
P
= 1 − s
12
1 − q + q1 − s
12
2 1 + 1 − s
12
1 − q + q1 − s
12
. There are two different aspects affecting firm 1’s disclosure decision. First, if the efforts
are strategic complements, disclosing is profitable because it leads firm 2 to exert a higher effort in equilibrium, that benefits firm 1. But, on the other hand, if λ is low enough, it is
in firm 1’s interest not to disclose in order to pay a lower transfer to firm 2. For λ λ
P
, the second effect dominates, leading to the existence of pooling equilibria.
6
However, for λ λ
S
, the first effect dominates, leading to the existence of separating equilibria. Finally, for λ ∈ [λ
S
, λ
P
], the three different types of equilibria coexist. Observe that as the subsidy increases, the region of pooling equilibria decreases. The
reason is that as the subsidy increases, the project becomes more profitable for firm 1 and the direct positive effect of disclosing increases. Finally, notice that λ
S
does not depend on q
6
Proposition 5.1 is obtained under the assumption that firm 1 has to decide whether or not to disclose the subsidy before the transfer takes place. If we allow that firm 1 may also decide to disclose the subsidy after the transfer
stage then, with strategic complements, it would always disclose the subsidy, whatever the value of λ. For λ ≤ 0.5, it would disclose after the transfer state, avoiding the payment of a higher T but still taking advantage of the
positive strategic effect of disclosing on the partner’s effort. on the other hand, for λ 0.5, it would choose to disclose before the transfer stage to take advantage of both the transfer payment and the strategic effect. Therefore,
under this alternative assumption, we would not obtain pooling equilibria under strategic complements efforts but as we will see below only under strategic substitutes.
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
