Effort and Performance in Public-Policy Contests

∂ x^*H             ∂x_L >         ∂² Pr_H        >   ∂² Pr_L

----> 0 and   —^l--0 ⇔--H-η n---—n„ n_τ .

∂I               ∂I <          ∂x_H ^{2 L H} < ∂x_L∂x_H ^{H L}

Notice that by Proposition 2(b), the conditions resolving the ambiguity
regarding the sensitivity of j’s effort to a proposed policy reform involve the three
elements of asymmetry between the contestants introduced in sections II and III:

(“substitution”) effect and the strategic own-stake
on the relationship between the ability-asymmetry
the normalized stakes-asymmetry represented by

3 ^ηj

_A 3 _{j      п}

—=- = ^z i . Specifically, by Proposition 2 , it can be easily verified that

_A2_{j ηi}

∕ⁿ

j

⇒ —-
∂I

To illustrate the economic interpretation of this corollary, suppose, for example, that
the HB player has a disadvantage in terms of his equilibrium ability (marginal
∂ ² Pr_H

winning probability), that is, -----— < 0 . By Proposition 2, when the proposed

∂x ∂x

HL

reform is of type (iv), an increase in I induces the LB player to increase his effort. In
this case the HB player’s effort is a strategic substitute to the LB player’s effort, so the
strategic substitution effect induces the HB player to reduce his effort. However, his
effort is a “normal” good, so the increase in his stake induces him to increase his
effort. The latter effect is dominant and the HB player also increases his effort, if his
advantage in terms of stakes, which is represented by the stake-asymmetry measure

^H is larger than his ability disadvantage, which is represented by the

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