The name is absent

hjmj + h_ε (ηj + aj + εj -
a^j) > ^hk^mk + ^hε(ηk + ^εk⁾ 1
^hk + ^hε J

Define the random variable

Our independence and normality assumptions imply that the prior distribution of ζj is
normal with mean

and variance¹³

2 ≡ ⁽ hε V ⁽ 1  -1 ^  ⁽ hε V ⁽ 1  1 ʌ          (4)

∖ ^hk + ^hε /  ∖ ^hk   ^hε∕    ∖^hj + ^hε /  ∖ ^hj   ^hε /

We denote this distribution by ψj (∙) with c.d.f. φ_j∙ (∙). The probability of j’s nomination
given ak = a^j_k is then

Pj(aj;^{aj, a}k^{, a}k) = P^r {c∙ < h + _h (aj^{- aj}) J = ^φj ɑ + h (aj ^{- aj}f)

The marginal impact of a_j∙ on j's expected payoff given a_k = a*_k is

Note that if c' (0) ≥ ψj (0) _h^h+h_ε Wj, then aj = 0.14

The first-order conditions for an equilibrium with a^j₁ , a₂^j > 0 are

^c'  ^j ■ (⁰) h1^hW^W1,

c' (aj) = φ2 (0) _r^h-_i-W2.
h2 + h_ε

Note that each of these conditions is a function of only one of the effort levels: in equi-
librium the principal correctly anticipates effort levels, which implies that given k indeed
chooses a_k^j , j ’s nomination probability is independent of the level of a^j_k. Our assumptions

¹³ Since the prior distributions of ζ1 and ζ2 have the same variance, we can simply denote this variance
by σ² , not using any subscript.

¹⁴ Since aj is j’s effort additional to the effort he would have exerted in the absence of the nomination
contest, it may well be that c' (0) > 0.

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