post efficient equilibrium.
Proposition 3. Consider the game in which the innovator and the competitor both receive the
same signal about the quality of the good to be innovated. There exists a mechanism which has truth
telling by both agents and which implements the ex post efficient outcome.
6. Market signals with bribes
We now consider an environment in which the innovator can bribe the competitor to misreport
the quality of the good. We show that in this environment, the equilibrium outcomes coincide exactly
with those in the environment in which no agent other than the innovator observes the quality of
the good. This result implies that patents are again optimal as in Proposition 1..
In what follows we again consider environment described in Section A.We begin by describing
how the possibility of bribes modifies the constraints that the social planner faces. We do so by
considering an arbitrary mechanism which consists of abstract action sets A for the innovator and Ac
for the competitor, actions a ∈ A and ac ∈ Ac, recommendations by the planner to innovate δ (aɪ),
length of patent granted to the innovator τ (a, ac), length of the patent awarded to the competitor
τc (a, ac), and the prizes T (a, ac) and Tc (a, ac).
We assume that the players can observe each other’s actions. We also assume that they can
agree, before the actions are chosen, to pay transfers (bribes) to each other contingent on the actions
chosen by the innovator and the competitor. We assume that these bribes are not observable to
the mechanism designer and that there are no limits to the size of the bribes. Let B (a,ac,θ~) and
Bc (a, ac, θ) denote the payments made by the innovator and the competitor so that
B (a,ac,θ) + Bc (a,ac,θ)=Q. (12)
Note that we assume that these bribes can be enforced. The payoffs of the agents are
augmented with the bribes. The revelation principle clearly holds in this environment so that any
Nash equilibrium of the arbitrary mechanism can be implemented by a direct mechanism. Let
v(θ,θ,θc ,δ(ty)
and Vc (θ,θ,θc,δ (Â))
denote the payoffs granted by the direct mechanism to the
innovator and the competitor. These payoffs are given by
V(θ, θ, θc, y) = δ (θ) [τ(θ, θc)π(^θ) - ^K + T(θ, 0c)] ,
(13)
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