A. Implementing ex-post efficient allocation
Let 0 denote the report made by the innovator and 5(0) the recommendation by the mech-
anism to incur the fixed cost K. (Recall that if the cost is not incurred, the innovator produces a
good of quality 0.) After the innovator produces the good, the competitor must submit a report of
the quality of the good. The competitor only observes the quality of the good produced. Let 0c
denote the report made by the competitor. A mechanism consists of reports made by the innovator
and the competitor and outcome functions 5(0), τ(0, 0c), T(0, 0c), Tc(0, 0c), where 5(0) denotes the
recommendation by the mechanism to incur the cost K ; τ (0, 0c) denotes the length of the patent;
T(0, 0c) denotes the prize to the innovator; and Tc(0, 0c) denotes transfer to the competitor.
The payoffs to the innovator induced by the mechanism are then given by
V(0, 0, 0c (y) , y) = 5(0) [τ(0, 0-0 - -K + T(0, 0c)] . (7)
In this formulation of the payoff to the innovator, V(0,0, 0c (y) , y), the arguments are, in
order, the true type of the quality of the good 0, the report by the innovator 0, the report by the
competitor 0c (y), and the decision of the innovator y to incur the cost K. The payoffs to the
competitor are given by Tc (0, 0c).
The incentive compatibility constraint for the innovator is given by
V(0,0,0,5 (0)) ≥ max V(0,0,0,5 (0)). (8)
e∈[o,e] v 7
Note that in this incentive compatibility constraint we have assumed that the competitor
reveals the information truthfully. This formulation of the incentive compatibility constraint fol-
lows from the revelation principle that states that the Bayesian equilibrium of any game can be
implemented as a truth-telling equilibrium of a direct mechanism.
The incentive compatibility constraint for the competitor is given by
^c
Tc (0,0) ≥ Tc(0,0 ).
An interim-efficient and the ex post efficient mechanisms are defined in the analogous way as
in the above. Note that since ex post efficiency assumes that the planner has the same information
as the private agents, the ex post efficient outcomes in the environment with and without market
signals are identical.
11
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