The name is absent

intuition that two people incurring equal disutility deserve equal rewards” (Kranich
1994, p. 178).¹¹

Definition 2 A policy is called affirmative action (AA) if:

ci(ei) = cj (ej) ⇒ pi (e) = pj (e) for all i = j.

For the class of contest games as defined by the CSF in eq. (2) the following relation
with respect to the policy weights (α₁^AA, . . . , α_n^AA) satisfies the definition of affirmative

αAA   α_jAA

~τr= =   ■ for all i = j.

βr βr            ^j

This relation is derived by using the following transformation of variables: z_i = c_i (e_i )
for all i ∈ N. As ci (ei ) is linear it can be inverted: ei = zi /βi . For the so transformed
model the condition in Definition 2 then states that if z_i = z_j∙ then p_i(z∕β) = Pj (z∕β),
where z∕β = (z₁∕β1,... z_n∕βn) denotes the vector of transformed individual effort.
Solving p_i (z∕β) = pj (z∕β) for z_i = zj implies that: α_i^AA(z_i ∕β_i )^r = α_j^AA(z_i ∕βj)^r which
has to hold for all values zi = zj . This condition is satisfied if the above mentioned
relation holds. The following normalization simplifies the subsequent analysis. As the
CSF is homogeneous of degree zero, there is no loss in generality if the weights are
normalized such that:

α^AA = β^r for all i ∈ N.                            (5)

The policy AA therefore generates a bias¹² of the contest success function in favor of
discriminated contestants in such a way that both contestants have the same probabil-
ity of winning the contest whenever they face the same disutility of effort. Note that
this definition requires that the affirmative action bias is implemented multiplicatively
through α_i^AA which increases the marginal efficiency of exerted effort for contestant i
and therefore changes the incentives for effort distribution. This type of affirmative

¹¹This quotation from Kranich (1994) justifies a related ‘equal-division-for-equal-work’ principle in his
model. The difference to the model presented here is that ‘equal work’ should be interpreted here
as equal disutility of effort as this is the relevant normative standard of comparison if contestants
are not responsible for the differences in marginal costs.

¹²In Clark and Riis (1998) it is argued that the anonymity axiom of Skaperdas (1996) should be re-
laxed because “in many situations, however, contestants are treated differently (due to affirmative
action programs for instance)” (Clark and Riis 1998, p. 201). The resulting CSF is asymmetric
as in eq. (2) but without any further specification of this asymmetry. Definition 2 can therefore
also be interpreted as a substitute of the anonymity axiom that entails now a specific normative
restriction with respect to the asymmetry of the CSF.

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