and aggregated effort does not only not exist but that both objectives are also closely
related. The result for the n -players case and the case with a partially informed contest
designer is not as straight-forward: a trade-off is unlikely to exist if the participation
decision of the contestants is not altered substantively through the implementation of
the affirmative action policy. The results for the individual comparison of equilibrium
effort are highly dependent on the distribution of the discrimination parameters.
However, the general idea of how the implementation of affirmative action affects
the incentives with respect to effort contribution can be summarized in the following
way:27 Discrimination is a source of heterogeneity between individuals in competitive
situations. The implementation of appropriate affirmative action ameliorates (at least
in the aggregate) this heterogeneity and makes individuals more similar. This increases
competitive pressure and therefore induces higher effort by all participants. However,
this argumentation only works if discriminated individuals are in fact the weak ones,28
if they are identifiable, and if participation effects are not too important. If these
requirements are satisfied the critique that affirmative action instruments have disin-
centivating effects on contestants and therefore adverse consequences for total effort
seems to be unjustified.
A Appendix
A.1 Equilibrium in the n-Player Contest Game
To construct the share function of contestant i, his expected utility function has to
be transformed in such a way that the contest can be interpreted as an aggregative
game in which the utility function of contestant i can be expressed as πi (zi, Z), where
Z = ∑i∈N Zi. Consider the following transformation that yields a transformed utility
function that is strategically equivalent to Eq. (9): denote zi = αiP ei which can be
27This argumentation must not be restricted to the specific model of contest games considered here.
In fact, in Che (2000) it is shown that the effort reducing effect of asymmetries, the so called
‘preemption’ effect, also exists for difference-form contests that include all-pay auctions as a
special case.
28In a previous version of this paper the contestants were also heterogeneous with respect to valuation
for which they were held ethically responsible. In this case the result in Proposition 2 only holds
if discriminated players are sufficiently weak because otherwise the preferential treatment of dis-
criminated players with high valuation would increase the de-facto heterogeneity (a phenomenon
which is also coined ‘reverse discrimination’).
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