P. A. GARAKANI ET AL.
54
has been considered. The aim of the current note is to
analyze whether the findings of the literature carry over
to the second type of contest. Considering a simple con-
test with discrete effort choices, we find that this is not
true. For instance, we find that the optimal information
policy may well depend on the prize spread. If the con-
test organizer leaves the contestants uncertain about their
initial heterogeneity, there is typically a pure-strategy
equilibrium where the contestants either choose low or
high effort for sure, depending on the prize spread.2 If
information is revealed to the contestants and they get to
know that they are heterogeneous, there is a mixed-
strategy equilibrium where each contestant chooses low
and high effort with positive probability. Hence, depend-
ing on whether or not contestants are expected to choose
high effort in the first situation (which in turn depends on
the prize spread), concealing or revealing information is
the preferred option. Related to this result we find that
the contest organizer sometimes prefers to reveal infor-
mation to the contestants if they are very heterogeneous.
As indicated before, this is because they may choose low
effort for sure when they do not receive any information.
2. Description of the Model and Notation
A principal organizes a contest between two agents
P
and . All parties are risk-neutral. The winner of
the contest receives the winner prize 1, while the loser
gets . Prizes are exogenously given. Denote by
12
the prize spread. The agent with the
higher performance wins the contest. If both perform
equally well, a fair coin determines the winner. Agent
’s performance
B
2
<ww
1
w
w:=ww
i(i =,)
B is given by
ii
=eyi
The variable denotes the agent’s effort.
Effort is costly and costs are defined as
i0,1e
ii
e=0=0c
and
ii
e=1= 0,2
w
cc
i
.
can be interpreted in
different ways. For instance, it can describe an agent’s
previous performances in the contest. Alternatively, it
may be used to describe a situation where the principal
favors one agent over the other (if AB
). Finally, it
may account for ability differences.
Under either interpretation, the principal should have
superior information concerning the realization of i
.
This is because she typically gathers the performance in-
formation, knows her preferences for the agents and may
be in a better position to judge, whether the agents are able
to handle certain tasks. To account for this, we assume
i
to be a random variable and the principal the only
one to observe its realization (before agents choose their
efforts). More concretely, we assume three states of na-
ture. We either have
1=,=1,0
AB
,
,0
2
or =0
3=0,1
p
. This means that each agent can be in the
leading position, but also that they may tie before choos-
ing their efforts3. The states occur with probability 1,
2 and 3, respectively. At the outset, the agents are
homogeneo us and, thus, .
p
p
13
While the principal privately observes the state of na-
ture, she can reveal her informatio n to the agen ts.4 In th is
context, we assume that she cannot misrepresent the in-
formation, i.e., she cannot lie about the state of nature.
For instance, if performance information is recorded
within a firm, the principal may withhold the records
from the agents, but she cannot forge them. Moreover,
the principal is restricted in that she can either inform
both agents about the state of nature or none of them.5
=pp
Summarizing, a strategy for the principal consists of a
triple
123
=,,
p
III, where
I
8
=,
() is a vari-
able indicating whether the principal reveals her infor-
mation to the ag ents () in state or not ().
In total, the principal has different (pure) strate-
gies some of which lead to the same outcome (see the
analysis in Section 3). We assume that the principal
cannot commit to a strategy, but chooses the revelation
policy that is optimal for her ex post, i.e., after the state
of nature has been realized. The agents’ strategies can be
written as a quadruple 123An
=1,2,3j
j
,,
=1
j3
I=0
j
I
2=
qqqq, with
qj
as
the agent’s effort choice if he is told to be in state
and n as his effort if the principal withholds her in-
formation from the agents.
q
2Hence, uncertainty imposed by the contest organizer has a simila
effect as noise in that both may induce the contestants to play a pure
strategy.
3Note that only the difference between A
and
has an effect on
the agents’ behavior. Hence, in the second state, we may also assume
1,1,=
AB
The principal chooses her strategy so as to maximize
the sum of expected effor ts. The agents choose their strate-
gies in order to maximize the expected payment minus
costs entailed by effort.
.
4Note that the contest outcome is not affected by another random vari-
able in addition to A
and
. Hence, if the agents get to know
these two variables, there is no uncertainty. The model results would
continue to hold if the contest outcome was affected by another noise
term, as long as the influence of this noise term on the outcome was
sufficiently low.
5A possible reason could be that
cannot prevent the agents fro
sharing information.
3. Model Solution
When agents decide about their effort, they trade-off the
higher effort costs from a positive effort with the in-
Copyright © 2011 SciRes. TEL