Effort and Performance in Public-Policy Contests

∂²Pr

₁ r_H

ability-asymmetry measure A H = ^H

∂x ∂x

HL

interpretations can be given to the conditions in Corollary 2.2 in all other possible
situations corresponding to the three types of reforms affecting the two players, given
that the HB player is advantageous or disadvantageous in terms of his equilibrium
ability.

In our setting, the response of one contestant to a change in the proposed
policy is ambiguous. A change in I may differently affect therefore the aggregate
∂²Pr_ι

efforts of the contestants. This implies that when ------≠ 0, under any type of a

∂x_ι ∂x
ιj

proposed reform the effect of a change in I on the aggregate effort X* = x *_H +x *_L is

∂**

x H ∂ x L

--+--, by (8) and Corollary 1.1 we get:

∂I    ∂I

Proposition 3:

That is, if ι’s effort is a strategic complement to j’s effort, then aggregate effort
increases with an increase in j’s stake. Aggregate effort also increases with I’s stake, if
the positive strategic own-stake (“income”) effect of player ι is larger than the
negative strategic rival’s-stake (“substitution”) effect of player j.

By (2) and (8) we obtain that:

∂X ^*    ∂ x^*H  ∂ x^*L

=+
∂I    ∂I ∂I

(9)

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