contemplates deviation to this value of θ. Incentive compatibility requires
0 ≥ T (0) - c (0 - 0) ≥ K - c0 ≥ K - c0.
Since K — c0 > 0, we have a contradiction. This mechanism is not incentive compatible. Suppose
now that the mechanism has innovation for some value of 0 <0*. Again, voluntary participation
requires that
T (0) ≥ K.
An innovator who has an idea of quality zero and deviates to this value of 0 will have a
profitable deviation as in the reasoning above. Q.E.D. ■
A. A simple example
We now consider a simple example which demonstrates that as the cost of manipulating the
signal rises, the length of the patent falls. To do so, we suppose that the quality of the ideas takes
three values: 0 < 0ι < 02. Suppose that the S (0ι) < K and S (02) > Sm (02) > K, and that c < ^∣.
From Proposition 5. we know that the mechanism must feature patents. Since S (0ι) < K, it is
optimal to have no innovation if the quality of the idea is 0ι. The interesting incentive compatibility
constraint is the one that ensures that an innovator of quality 0ι does not misreport the quality of
the idea and manipulate the signal. This constraint is given by
0 ≥ τ (02) π (01) - K + T (02) - c (02 - 0ι) . (21)
The incentive compatibility constraint that the innovator of type 0 = 0 does not misreport
the quality of the idea and manipulate the signal is given by
0 ≥ T (02) - c (02 - 0). (22)
Note that this incentive compatibility constraint is also the incentive compatibility constraint
for the innovator with the idea 0ι who chooses not to incur the cost and to misreport the signal.
The voluntary participation constraint for type 02 is given by
τ (02) π (02)+ T (02) ≥ K.
(23)
21