player production economy where the jointly produced output is shared according to a
‘division rule’. He introduces a normative requirement for the class of feasible division
rules which is phrased equal-division-for-equal-work principle5 and shows that there
exist feasible division rules that satisfy this principle in combination with Pareto-
efficiency. In contest games, however, the notion of Pareto-efficiency is meaningless
because there is no production, i.e. the contested prize does not depend on the exerted
effort of the contestants. Therefore, a Pareto-ranking of the outcomes of the two
normatively defined policies is pointless in a contest game framework. Instead, the
two policy alternatives are evaluated with respect to the total equilibrium effort that
they generate.6
Contrary to Sowell's prediction, it is shown that in the two-player contest game the
optimal individual response to the implementation of affirmative action would be to
increase individual effort level in comparison to the unbiased contest game (irrespective
of the fact whether the individual is discriminated or not). However, relaxing the
restriction on the number of players is not innocuous: the result for the two-player
case can only be sustained in the n-player contest game if the underlying heterogeneity
is not too severe because otherwise participation effects dominate incentive effects. As
the model is kept sufficiently simple to facilitate analytical tractability, it is too stylized
to give any sort of direct policy implications. Nevertheless it shows that a trade-off
between affirmative action and aggregated effort, as stated by Sowell, may not exist,
especially if participation effects are not an important issue.
The contest model is formulated in general terms to reflect in a stylized way a variety of
situations in which the implementation of affirmative action can have consequences on
the incentive structure of effort provision. Possible real world examples of contest-like
of contestants compete for positions in simultaneous pair-wise tournaments. There, the analysis
is focused on the comparison of group-sighted and group-blind affirmative action policies without
addressing explicitly the incentive effects of affirmative action versus unbiased tournament rules.
5 The subsequently stated definitions of the two policies are modified versions of this principle in the
sense that they now capture the two different normative perceptions of the heterogeneity of the
contestants. Therefore, the interpretation of ‘equal work’ has a different meaning depending on
the perceived underlying reason for the heterogeneity.
6 This interpretation of exerted effort as being socially valuable is the crucial difference to the ex-
tensive literature on rent-seeking contests (comp. the literature survey in Nitzan (1994) and a
collection of related articles in Lockard and Tullock (2001)). There, exerted effort is usually in-
terpreted as pure social waste, while in situations where affirmative action is applied it is more
appropriately characterized as socially valuable (which is also suggested by the quotation of Sow-
ell). In the recent literature on sport contests effort, i.e. the performance of the athletes, has a
similar interpretation; see Szymanski (2003).