Prizes and Patents: Using Market Signals to Provide Incentives for Innovations

The incentive compatibility constraint for the innovator is given by

V(0, θ, θ, δ (0)) ≥ max V(0, fl, θ, δ (fl)),                                (16)

θ∈[o,θ]                   ^{v 7}

and the incentive compatibility constraint for the competitor is given by

V^c(0,0,0,δ (0)) ≥ max V^c(0,0,0^c,δ (0)).                         (17)

θ^c∈[o,θ]

We denote the sum of the payoffs to the innovator and the competitor by

V (0) = V (0,0,0, δ (0)) + V^c (0,0,0, δ (0)).

The bribe-proofness constraint is now given by

V (0) ≥ max ^[V(0, 0,0^c,δ (0)) + V^c(0, 0,0^c,δ (fl))] .
θ,θ ^l                      ' '                               ' ' ^j

The social planner’s payoffs in the truth-telling equilibrium are now given by

W = ʃ {δ(0)[τ(0) S^m(0) + (l - f(fl)) S(0) - K]} dF (0),                 (18)

where

f(fl) = τ (0)+ τ^c (0) .

The social planner’s problem is to maximize (18) subject to (15), (16), (17), and the analogs
of the voluntary participation and no money pump constraints. We now show the proposition that
characterizes the social planner’s problem.

Proposition 4. (Optimality of patents with bribes) The solution to the social planner’s prob-
lem with bribes coincides with that in the environment with no market signals problem. In particular,
the solution to the social planner’s problem coincides with the outcome described in Proposition 1.,
in that the interim-efficient mechanism has no prizes T (0) = 0, Vfl, and a constant patent length
τ (0) = τ, V0.

Proof. Consider a relaxed version of the social planner’s problem which does not impose the
individual incentive compatibility constraints and which replaces the voluntary participation and

17

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