option to rescind on his previous report at a cost. The first inequality ensures that if ^∣ is the true
report and θc is not, the innovator will choose alternative A. The second inequality ensures that
if θc is the true report and θγ is not, the innovator will choose alternative B. The third inequality
ensures that if the competitor tells the truth, the innovator also tells the truth and finds it optimal
not to go to Stage 2. Since four choice variables need to satisfy only three inequalities, clearly we
can choose these four variables.
Now we turn to the transfers to the competitor. If both agents report the same value of θ in
Stage 1, the competitor receives a transfer of zero. If the reports differ, then the competitor pays a
tax — T if the innovator chooses an alternative A and receives a transfer T if the innovator chooses
an alternative B.
We claim that this mechanism has a unique equilibrium that is truth telling. Suppose that
the equilibrium for some realized value of θ involves these two agents reporting a common value of
θ = θ. Under this supposed equilibrium, the payoff of the competitor is equal to zero. Now consider
a deviation by the competitor to the true report, that is setting θc = θ. Under this deviation,
the mechanism requires the players to proceed to Stage 2. Inequality (10) guarantees that in this
subgame, the innovator will optimally choose the alternative B. Recall that if the innovator chooses
the alternative B, the competitor receives a positive transfer. Thus, such deviation is profitable and
the equilibrium cannot have both agents reporting a common value θ = θ.
Now suppose that the innovator reports the truth and the competitor lies and reports a value
of θ = θ. The mechanism requires that the players move to Stage 2. In that stage, inequality (9)
guarantees that in Stage 2, the innovator will choose option A. The competitor’s payoff is then given
by the tax that the competitor must pay. A deviation of the competitor to reporting the truth gives
the competitor a zero payoff which dominates misreporting. Thus, we cannot have an equilibrium
in which the innovator tells the truth and the competitor lies.
Next suppose that the competitor reports the truth and the innovator lies and reports a value
of θ = θ. The mechanism requires that the players move to Stage 2. In that stage, inequality (10)
guarantees that the innovator will choose option B. The innovator’s payoff is then given by the
left-hand side of (10) equal to the right-hand side of (11). Consider a deviation from the supposed
equilibrium in which the innovator reports the truth. The payoff to this deviation is given by the
left-hand side of (11). Thus, this deviation is profitable and the game cannot have an equilibrium
in which the competitor reports the truth and the innovator lies.
This argument establishes the following proposition on a unique implementation of the ex
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