Effort and Performance in Public-Policy Contests

Baik (1994). Here the parameter σ represents the asymmetry between the lobbying
abilities of the two players. Note that when σ <1 the HB player has an ability

disadvantage relative to the LB player. It can be shown that under this particular

increasing in x _i , then

'x ≥ 0 ^d' ≤ 0 ⇔ PrH ≤ 1/2 .
∂n_H         ∂n_L

This third corollary generalizes Proposition 1 in Baik (1994).

B. Complete incidence: Policy reforms affecting both stakes

When a change in I affects the stakes of the two contestants, as in reforms type (i),
(iv) and (v), η_L and η _H are positive or negative. By the fundamental equation (8),
when the contestants’ efforts are independent, the sensitivity of every contestant’s
effort with respect to a proposed policy reform is always unequivocal. When the
contestants’ efforts are not independent, the sensitivity of one of the contestants’
effort with respect to a proposed policy reform is always unequivocal because the sign
of his strategic rival’s-stake (“substitution”) effect is equal to the sign of his strategic
own-stake (“income”) effect. The sensitivity of his opponent’s effort with respect to
the proposed policy reform is ambiguous, depending on whether his strategic own-
stake (“income”) effect is larger than, equal to or smaller than his strategic rival’s-
stake (“substitution”) effect. Using (8) we thus get

declining in his effort . This requires additional assumptions on the first and second derivatives of the
function h(x_i ) .

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