The name is absent

environments in which affirmative action is implemented are:⁷ university admission,
in which applicants compete for places in a university program by means of their high
school grade point average and minority students get some kind of bonus; fixed bonus-
payment tournaments within a firm where the bonus is payed to the employee with
the highest sales performance and discriminated employees might get some limited
advantage; and even sport contests, for example horse riding, in which jockeys that
weigh less than their competitors are forced to carry additional weight.

2 The Model

Affirmative action instruments are usually applied in situations of competitive social
interaction. The competitive structure of these situations can be captured by a contest
game in which contestants compete for an indivisible prize. The contestants can
increase their respective probability of winning the contested prize by exerting more
effort. This feature seems to be appropriate to model the basic structure of the above
mentioned examples because there exists a relatively high grade of discretion on the
side of the organizer of the competition. This is reflected in a contest game in which
contestants face a probabilistic outcome. To guarantee analytical tractability and
closed form solutions, the model is formulated under complete information, i. e. the
only element of uncertainty is the final winner of the contest.

2.1 The Contestants

Let N = {1, 2, . . . , n} denote the set of individuals that compete against each other in a
contest game. Each contestant i ∈ N exerts an effort level e_i ∈ 'h^v' and takes the effort
level e_-i = (e₁,..., e_i-1, ei₊1,..., e_n) ∈ ¾+~¹ of its rivals as given. Additionally, it is
assumed that all contestants are risk-neutral and have the same positive valuation V
for the contested prize. The only element of heterogeneity among the contestants is the
respective ‘cost function’ that captures the disutility of exerting effort ei which depends
additionally on parameter β_i that (potentially) reflects the degree of discrimination of
contestant i. It is assumed that this cost function is linear in e_i and multiplicative in
βi for all i ∈ N , with βi normalized in such a way that for the most able contestant

⁷ For empirical results with respect to the consequences of different affirmative action policies com-
pare the survey in Holzer and Neumark (2000).

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