A mechanism is incentive compatible if for all
(M
it satisfies
V(0,0,δ (0)) ≥ max V(θ,θ,δ(θ)).
(4)
0∈[o,0] v 7
In this formulation of the incentive compatibility constraint, note that we require that an
innovator who follows the recommendation of the planner, δ (0) , and reports his true type gets a
higher payoff than an innovator who deviates from the recommendation of the planner and chooses
7 = δ (0) or misreports the type θ, or does both.
A mechanism satisfies voluntary participation if
V(θ,θ,δ (0)) ≥ 0. (5)
We say that the mechanism satisfies a no money pump assumption if
T (0) = 0. (6)
This assumption is motivated by the following considerations. The economy has a large number of
innovators with ideas of value 0 = 0. If the mechanism gave positive prizes T to all innovators, the
society will then not be able to pay off for all of these ideas of no value.
We now formally define an interim-efficient mechanism.
Definition 1. The mechanism is interim efficient if it maximizes social surplus (3) subject to
incentive compatibility (j), the no money pump assumption (6), and voluntary participation (5).
We then have the following proposition.
Proposition 1. (Optimality of uniform patents). The interim-efficient mechanism has a con-
stant patent length τ (0) = τ, V0 and no prizes T (0) = 0, V0.
Proof. We first show that there is some critical threshold 0* such that δ (0) = 0 for 0 < 0*, and
δ (0) = 1 for 0 ≥ 0*. The argument is by contradiction. Suppose that 0ι < 02, δ (0ι) = 1, and
δ (02) = 0. Consider the incentive compatibility constraint for the innovator who has an idea of
quality 02 and contemplates a deviation to reporting 0ι. Under the supposition that δ (02) = 0, the
payoff of the innovator of truth telling is equal to 0. Using the incentive compatibility constraint,