The name is absent

where aj ∈ [0, ∞) is j’s effort in the nomination period, unobservable for the principal and
agent k = j . εj is a stochastic noise term, and we assume that ε1 and ε2 are independently
and normally distributed with zero means and precision h_ε .

We focus on the agents’ efforts aimed at winning the nomination contest here, ab-
stracting from the incentives generated by their work contracts and other career con-
cerns. It would be straightforward to integrate this analysis into a richer model. Agent
j = k ∈ {1, 2} maximizes

Πj  aj ; a_j^e, ak, a^e_k  = Pj  aj ; a_j^e, ak, a^e_k  Wj - c(aj),

where Pj aj; a_j^e, ak, a^e_k is the probability of j’s nomination as a function of j’s anticipated
effort a^e as well as k’s actual and anticipated effort levels a_k and a^e_k. c (•) : R+ → R+ is
an increasing and strictly convex function measuring the disutility of effort. We treat Wj
as exogenous here, but at the end of this section we will discuss ways in which Wj may
be expected to depend on j ’s characteristics, in particular hj .

The principal’s objective is to nominate the most skillful agent; after observing y₁ and
y2 he will hence select j if and only if¹²

E[ηj | yj] > E[ηk | yk].

Denote by (ɑɪ, a2) the equilibrium effort choices. In equilibrium, each agent’s effort
choice must be optimal given the other agent’s effort choice and beliefs, and the principal
must correctly anticipate effort choices, i.e., a^e = a* for j = 1, 2.

Given our normality and independence assumptions, the learning process about each
agent’s skill is well-known. For a_j^e = a_j^* , the posterior distribution of ηj will be normal
with mean

hj + hε

and precision hj + hε .

Let us now consider j ’s effort decision at the beginning of the period. From (2) it
follows that, given a_k = a^*_k , if j chooses aj then he will be nominated with probability

¹²We implicitly assume here that the principal is risk-neutral, and that the cost of incentive provision
once the agent is nominated, i.e., during the Euro Cup in our soccer example, is unrelated to the agent’s
preceived ability. If h1 = h2, then there exists a biased tournament as in Meyer (1991, 1992) that is
equivalent to the principal’s decision rule. In this biased tournament, the contestant with the lower prior
reputation has to outperform the other agents by a given amount in order to win. For h1 = h2 , the rates
at which the principal updates his beliefs about the agents’ skills as a function of observed outputs differ,
and therefore there is no such direct equivalence.

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