the first interval could be empty if n - 1 > β which depends on the relevant underlying
distribution. □
The set of contestants that individually exert more effort under the AA policy is not
connected. The following argumentation provides an intuition for this result: Consider
first a (potentially hypothetical) contestant k with a marginal cost that is identical to
the mean of the total distribution: βk = ∕β. Under policy AA this would imply that
contestant k is favored by αAA = Д Normalizing the vector (αAA,..., αAA) yields
the equivalent vector αt = (αAA∕β,..., αAA∕β). For contestant k this would imply
no distortion under AA because α'k = αAA∕β = 1. Additionally, he knows that under
AA contestants with higher marginal costs than him are favored (in average) to the
same amount as contestants with lower marginal costs are handicapped. Therefore,
his equilibrium effort level is not altered. Contestants with higher marginal costs than
contestant k are favored under αz, i.e. their efficiency of effort in the CSF is increased
(αli > 1 for i > k) which implies that they exert higher effort level. The contrary is
true for contestants with less marginal cost than contestant k : they are handicapped
(αli < 1 for i < k) which reduces their efficiency of effort and therefore also their
equilibrium effort. However, there exists a counter effect for contestants with very low
marginal cost which becomes dominant for some cut-off value. This counter effect is
due to increasing competitive pressure for those highly effective contestants because
they are more handicapped under AA than their competitors. The cut-off marginal
cost value is exactly at βc ≡ β∕(n — 1). Contestants that have a lower cost parameter
than contestant c will therefore exert higher equilibrium effort under AA than under
ET.
5 An Extension: Group Contests
In the last section the implementation of the AA policy was based on a bias of the
CSF that was individually specified for each contestant. However, the implementation
of affirmative action policies is usually not based on individual characteristics, but
on group membership, e.g. minority, sex, race etc. Reasons for this phenomenon
could be incomplete information with respect to individual discrimination, or simply
the fact that group members are sufficiently homogeneous to treat them identical.
In the following section the latter aspect is analyzed while in the next section the
informational requirements of the contest designer are relaxed.
The following model is a simplified version of the n -player contest game with the
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