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

The no money pump assumption and the voluntary participation constraints for type 0 and
type 0ι imply that

T (0) = T (0ι) = 0.

The social surplus is given by

τ (02) S^m (θ₂) + (1 - τ (0₂)) S (0₂) - K.

Clearly, social surplus is maximized by making τ (0₂) as small as possible subject to the
incentive compatibility and the voluntary participation constraints. Since reducing τ (02) relaxes
(21), it follows that the voluntary participation constraint (23) must be binding so that

T (02) π (02)+ T (02) = K.

Substituting for T (02) from (25) into (21), we have

0 ≥ τ (02) π (0ι) - τ (02) π (02) - c (02 - 0ι).

Since the right side of this inequality is strictly negative, it follows that (21) is not binding at the
optimum. Thus, (22) and (23) must be binding so that T (02) = c02. From these constraints we
have

τ (02) = K^-T∙                             <²⁶>

π (02)

We have shown that the length of the patent τ (02) is strictly decreasing in the manipulation
cost c.

8. Limitations of Kremer’s mechanism when manipulation is possible

An influential article of Kremer (1998) describes a mechanism intended to exploit informa-
tion that other market participants may have regarding the value of the innovation. This auction
mechanism is an example of a possible implementation of the optimal allocation in the general
mechanism design problem described in Section 5. In this section, we describe how market signals
may be manipulated in such mechanism.

Kremer’s mechanism is as follows. A patent holder has the option of choosing to be a part
of the auction mechanism. The government uses a second price auction. The winner of the second

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