Prizes and Patents: Using Market Signals to Provide Incentives for Innovations

Let S (0*) = K denote the threshold value of the quality of the good such that if 0 > 0*,
the full information efficient mechanism requires that the good be innovated, δ (0) = 1. If 0 ≤ θ*,
then the good is not innovated, δ (0) = 0. We then have the following proposition. We show that if
the manipulation costs are sufficiently high, patents are not optimal. If the manipulation costs are
sufficiently low, the patents are used in any efficient mechanism.

Proposition 5. If c > ^, then the solution to the social planner’s problem can be implemented
with prizes alone. If c < —-, then the solution to the social planner’s problem necessarily requires
using patents.

Proof. First, suppose that c > ^f. Consider the following mechanism that sets T (0) = K if 0 > 0*;
T (0) = 0, otherwise; δ (0) = 1 if and only if 0 > 0*. We will show that this mechanism is incentive
compatible. Consider a reporting problem of an innovator with the quality of idea 0 < 0*. Truth
telling yields a payoff of zero for this innovator. Suppose that this innovator deviates, claims that
the quality of his idea is 0 > 0* and produces a good of quality 0. The payoff from such deviation
is given by

V^m (θ, 0,1) = -K + K - c (θ - 0) = -c (θ - 0) < 0.

Thus, this deviation is not incentive compatible.

Suppose next that the innovator deviates and claims that the quality of the idea 0 > 0* and
does not incur the cost K, thereby producing a good of quality 0. The payoff from such a deviation
is given by

V^m (θ,θ, 1⁾ = K - c ⁽0 - 0⁾ ≤ K - c0* ≤ 0.

Thus, this deviation is not incentive compatible either.

Next suppose that c < у. The proof is by contradiction. Since a mechanism which only uses
patents is feasible and has innovation for some values of 0, the welfare-maximizing mechanism also
has innovation for some value of 0. Suppose that for some value of 0 > 0*, the mechanism specifies
δ (0) = 1 and some prize T (0) . Voluntary participation implies that

T (0) > K.

Consider the incentive compatibility constraint for the innovator who has an idea of quality 0 and

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