by the biased CSF). As the contestants are more similar under AA, the competitive
pressure is higher which implies higher equilibrium effort by both contestants.17
In fact, the bias that is induced by AA for the two-person contest game yields a
level playing field, i.e. the contestants are as similar as possible under this set-up.
Therefore, the policy AA also generates the maximal aggregated effort even for a
contest game that is not restricted by any normative constraint. In other words, if the
objective would solely be the maximization of total equilibrium effort by implementing
an appropriate weight c^2 then this weight would coincide with the bias that is required
by the AA policy.18
Proposition 2 The policy option AA generates the maximal sum of equilibrium effort
in the two-player contest game.
Proof : Consider the sum of equilibrium effort for an arbitrary parameter c2 that favors
the discriminated contestant: E* = , α2βrr.2 β+1 rV. This expression is maximized for
(α2+β2r)2 β2
α^2 = βr which coincides with αAA = βir for i = 1, 2.□
2 ii
Opponents of affirmative action policies claim that those policies could result in less
aggregated effort level. The last two propositions reveal that in the above specified
two-player contest this concern is not justified. Instead, both contestants will exert
higher effort levels in equilibrium if they face affirmative action. In fact, as it was
shown in proposition 3, the affirmative action bias even leads to the highest possible
level of total equilibrium effort. In the next section it is analyzed if these results are
also valid for contest games with more than two players.
4 The n-Player Contest Game
Contrary to the two-player case the derivation of the equilibrium and the proof of
existence and uniqueness for the n -player contest game are more involved because
not all contestants will always exert a strictly positive effort level in equilibrium.19
17 Similar results are known, for example, from the literature on optimal auction design: A revenue
maximizing auction implies also the favoring of weak bidders (comp. McAfee and McMillan 1989).
18 Nti (2004) introduces a 2-player contest game with different valuations and a CSF of the form
αiei+γi
Σi=1,2 αiei + γi .
pi (e) =
In this set-up, total equilibrium effort is maximized if γ1 = γ2 = 0 and
the multiplicative parameters (α1 , α2) balance the heterogeneity of the valuations.
19 This implies that first-order conditions that were used in the two-player contest to characterize the
equilibrium are not feasible here because the equilibrium might be non-interior. The approach
11