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Kim: Endogenous Choice of a Mediator
utilities among all incentive feasible mediators, and is the one associated with the lowest probability
on war outcome among all interim incentive efficient mediators. Note that when ¯p(s) ∈ (0.36, 0.45)
(Case 3 ), µ y,z (d 0 |ss) ≡ z is such that U 1 (µ y,z |w) = U 1 (µ y,z , s|w), where z can take values from
[0, ¯z(¯p(s))] depending on y and ¯p(s). When µ y,z (d 0 |sw) ≡ y = 1, the corresponding probability on
war for t ∈ {ss} would be ¯z(¯p(s)) = 11¯p(s)−4
7¯p(s)
, which is increasing in ¯p(s), depicted as an orange
dotted line in Figure 6.1.
When each player is known to believe that the probability of the strong type s is 0.15, i.e.,
¯p(s) = 0.15 and ¯p(w) = 0.85; then S(Γ) = {µ y,z |y ∈ [ 5 /17, 1] , z = 0}. Therefore, the set of interim
incentive efficient utility allocations between the strong and the weak type is a line in R 2 with end
points (U 1 (µ y,z |s), U 1 (µ y,z |w)) as follows: (0, 4.14), (0.6, 3.4). 26 The first of these allocations is implemented
by the unique ex ante incentive efficient mediator µ 5/17,0 . The second of these allocations
is implemented by µ 1,0 . For illustrative purposes, consider the utility allocation (0.26, 3.82) that
can be implemented by µ 0.6,0 .
The type-contingent expected payoffs from hiring these mediators are depicted in Figure 6.2
with the red dots that correspond to the probability that each mediator chooses d 0 for t = {sw, ws}.
The ex ante expected payoffs for each of the three mediators are also indicated.
Figure 6.2: Conditional Expected Payoffs when ¯p(s) = 0.15.
26 Since players are symmetric, without loss of generality, I focus on player 1.
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