results extend readily to the case in which this cost is drawn from some distribution, say, G(K) and
is private information to the innovator. To see this extension, consider a mechanism in which the
innovator’s prize is given by the social surplus if the innovator’s and competitor’s reports agree, so
that Ti(θ, θ) = S(θ) and the innovator receives no prize if the reports disagree so that Ti(θ, θc) = 0
if θ = θc. Clearly, truth telling is incentive compatible and the mechanism implements the efficient
allocation in the sense that δ(θ) = 1 if and only if S(θ) ≥ K.
B. Unique implementation of prize mechanisms
The mechanism that we have discussed uses information from the competitor to reward the
innovator. Under our particular mechanism, the competitor is indifferent about what information
to report. Truth telling is one of the equilibria of the game. Typically, the game has many other
equilibria. A natural question is whether we can design a mechanism which is ex post efficient
and has a unique equilibrium. Here, we adapt the mechanism of Moore and Repullo (1988) to our
environment. We show that such a mechanism has a unique subgame-perfect equilibrium in which
both the innovator and the competitor report the truth.
The mechanism has two stages. In Stage 1, the innovator and the competitor make reports
to the planner. Denote the report of the innovator by θi and that of the competitor by θc. If
θi = θc, equals say θ, then implement the ex post efficient outcome associated with the common
report θ. If θi = θc, then move to Stage 2. In Stage 2, the innovator is given a choice between
two alternatives, denoted by A and B. In each alternative, the innovator is granted a patent with
the length μq (0i, θc) and μβ (θi, θc) and prizes Tq (0i, θc) and Tb (0i, θc) chosen to satisfy for all
(θi,θc)
max '. (θi,θc) π (θi) - K + Ta (θi,θc) ; Ta (θi,θc)} (9)
> max {μβ (0i,0c) π (0J - K + Tb (¾0c) ; Tb (θi, θc)} ,
max {μB (θi, θc) π (θc) - K + Tb (0i,0c) ; Tb (¾0c)} (10)
> max {μq (¾ 0c) π (θi) - K + Tq (¾ 0c) ; Tq (θi,0c)} ,
T (θ,θ) - K> max {μB (θ, θ) π (θ) - K + Tb (θ, θ) ; Tb (θ, θ)} . (11)
The basic idea behind this mechanism is that in the second stage, the innovator is given an
13
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