In the following proposition, we show that the patents are never optimal. In fact, the full
information optimum can be achieved solely with prizes.
Proposition 2. (Optimality of prizes) In the environment with market signals, the interim-
efficient mechanism is ex post efficient.
Proof. Let the planner’s recommendation be to produce the good when the social value is higher
than fixed costs: δ (θ) = 1 if S (θ) ≥ K ; δ (θ) = 0 otherwise. Let T1 (θ,θ) ≥ K if θ = θc; T1 (θ, θc) = 0
if θ = θc. Let T2 (0,0c) = 0. In other words, implement the full information outcomes associated
with the value of θ only if both agents report that same value of θ. If the agents disagree, then give
the innovator a transfer equal to zero. The competitor always receives the same transfer regardless
of his report. Then the best response of the competitor is to report the value of the innovated goods
truthfully. Q.E.D. ■
Note that above we restricted the planner to award the patent only to the innovator. A more
general setup would allow the planner to reward the competitor with the patent. This restriction is
without loss of generality, since Proposition 2. shows that the planner can achieve the full information
outcome.
So far, we have assumed that the competitor receives the same signal as the innovator.
Suppose now that the competitor receives a noisy, but unbiased, signal s of the quality of the
good so that E(0∣s) = s and that E(s∣0) = θ. Consider a mechanism which sets the prize to the
innovator Tι(θ,s) = s if S(s) ≥ K and 0 otherwise and sets the transfer to the competitor to 0.
Since the innovator is risk-neutral, this mechanism yields the ex post efficient level of innovation as
a truth-telling outcome.
The competitor’s report also has an immediate market interpretation and a practical appli-
cation. Consider the simple market setup described above in which the inverse demand for the good
is given by p = D (q, θ) and c is the marginal cost of production. Suppose the market consists of
a large number of producers, all of whom can produce the good at marginal cost. The mechanism
designer then makes the knowledge of how to produce the good freely available to all producers
and asks each producer to report sales of the good. Since the price p equals the marginal cost
of production c in a competitive market, aggregate sales q can then be used to uncover the mar-
ket size parameter θ. Another example of the practical implementation of this mechanism is the
patent-buyout mechanism in Kremer (1998) that we describe in detail later.
Note that we have also assumed that the cost of innovating is known to the designer. Our
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