Proposition 1 and its corollaries generalize the comparative statics results of Baik
(1994) and Nti (1999) that focus on the effect of changes either in the value of a
contest prize in symmetric contests or in one of the contestants’ valuation of the prize
in asymmetric contests, assuming special forms of our general contest success
function. Propositions 2 - 5 present the comparative statics results in the extended
setting where the proposed public policy determines the prize system: the stakes of
the two interest groups. All the results hinge on a fundamental equation that stresses
the significance of the relationship between the strategic own-stake (“income”) effects
and the strategic rival’s-stake (“substitution”) effects corresponding to any change in
the proposed public policy. We clarified how this relationship is determined by the
three types of asymmetry between the contestants. In particular, we specified the
asymmetry conditions under which a more restrained government intervention that
reduces the contestants’ prizes has the perverse effect of increasing their aggregate
lobbying efforts. This result complements the related findings of Baye et. al (1993)
and Che and Gale (1998) that were established in the context of all-pay auctions.
While these scholars focused, respectively, on constraints on the set of contestants and
on caps on lobbying expenditures as possible means of reducing the asymmetry
between the contestants, we emphasize the role of public policy reforms in generating
direct changes in stakes-asymmetry and indirect changes in ability-asymmetry
between the contestants.
The public-policy contest that we studied has numerous applications. It seems
to us that it can constitute a useful basic building block in a more general theory of
endogenous public- policy determination. In such a theory the contestants themselves
could determine the two competing policies. Alternatively, another player, naturally
the government, could design the contest and control the prize system by determining
the proposed policy reform. Such a designer might be solely concerned with the
aggregate efforts of the contestants (the lobbying expenditures or the campaign
contributions), as in Baye et. al. (1993). But, of course, he may have broad objectives
that take into account the aggregate efforts of the contestants as well as their welfare
(expected payoffs), as in Epstein and Nitzan (2001a), Grossman and Helpman (1994)
and Hillman (1982).
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