Effort and Performance in Public-Policy Contests

∂² Pr_H        ∂² Pr_L

2   η LnH ⁺ ——n HnL

∂x           ∂x

HL

This proposition states the condition that resolves the ambiguity regarding the
sensitivity of aggregate effort with respect to a change in I . The condition clarifies the
role of stakes-asymmetry and ability-asymmetry between the contestants. It implies,
in particular, that even under the most restrained type-(v) policy reform that reduces
the stakes of the two contestants, it is possible that the two contestants are induced to
increase their aggregate effort. This occurs when the negative rival’s-stake
(“substitution”) effect of the contestant who is induced to increase his effort more
than counterbalances the sum of the two positive own-stake (“income”) effects and
his opponent’s positive substitution effect. Alternatively, if the LB player’s effort is a
substitute to the HB player’s effort, a sufficiently high reduction in the normalized
A³

stakes- asymmetry, a sufficiently high value of A ^h/ 2 , would induce the LB player
Ah

to increase his effort such that aggregate effort is increased. When the HB player’s
effort is a substitute to the LB player’s effort, a sufficiently small reduction in the
3

normalized stakes- asymmetry, a sufficiently small value of A ^h/ 2 , would induce
Ah

the HB player to increase his effort such that aggregate effort is increased. The fact
that a reduction in stakes-asymmetry can give rise to perverse effort incentives have
been noticed by Baye et. al. (1993) and by Che and Gale (1998). The former scholars
have noticed that a politician who designs a contest may find it in his interest to
exclude certain lobbyists from participation in the lobbying process - particularly
lobbyists valuing most the prize - because this increases the lobbying efforts of the
remaining contestants. The latter scholars have noticed that asymmetric limits on
exerted effort can also have the effect of increasing the aggregate efforts of the
contestants. We show that in a public-policy contest, under a sufficiently high or a
sufficiently low reduction in stakes-asymmetry, the most restrained government
intervention that takes the form of a type-(v) policy reform that reduces the prizes of
the two contestants may have the perverse effect of increasing their aggregate efforts.

Let us finally consider how a change in the proposed policy affects the
performance of the contestants, their probability of winning the contest:

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