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Kim: Endogenous Choice of a Mediator
Proposition 2. The unique ex ante incentive efficient mediator in S(Γ) is
When p ′ ≤ p ∗ , (a) µ y(¯p(s)),0 for Case 1; (b) µ 0,0 for Case 2, 3 & 4.
When p ∗ < p ′ , (a) µ y(¯p(s)),0 for Case 1 ′ ; (b) µ y(¯p(s)),z(¯p(s)) for Case 2 ′ ; (c) µ 0,0 for Case 3 & 4.
Proposition 2 gives the best mediator in an ex ante sense. The unique ex ante incentive efficient
mediator is the one who puts the lowest probability on war among all of the interim incentive
efficient mediators. Note that µ 0,0 is such that µ 0,0 (d 1 |t) = 1, ∀t ∈ T , which can be interpreted
as a peaceful mediator who always implements a peace outcome regardless of the players’ types.
Therefore, a peaceful mediator is the one who never creates an impasse that prevents an agreement.
The following Lemma 3 gives the interim welfare ordering in S(Γ).
Lemma 3. For each Case 1, 1 ′ , 2, 2 ′ , and 3, µ y,z is ex ante Pareto superior to µ y ′ ,z ′
if and only
if µ y,z gives strictly lower interim expected utility for the strong type and strictly higher interim
expected utility for the weak type.
Corollary 2. Suppose that ¯p(s) < p ∗∗ . Then, there exist multiple interim incentive efficient mediators
in S(Γ) who are not ex ante incentive efficient. Moreover, the one that is ex ante Pareto
inferior to any other mediators in S(Γ) is µ 1,o when ¯p(s) ≤ p ∗ and µ 1,¯z(¯p(s)) when ¯p(s) ∈ (p ∗ , p ∗∗ ),
which gives the highest interim payoff for the strong type.
Corollary 2 follows from the previous results. It suggests that there are multiple mediators in
S(Γ) who will, if chosen, mediate players according to some incentive feasible mechanism that is
not necessarily ex ante incentive efficient. The interim but not ex ante incentive efficient mediator
can be considered “bad” in the sense that it sometimes allows players to fail to reach a negotiated
settlement and to go to war with higher probability than the ex ante incentive efficient mediator.
The “worst” mediator, who puts a higher probability on war than any other interim incentive
efficient mediator, is the one that can be described as being the farthest away from the ex ante
incentive efficient mediator but gives the highest interim utility to the strong type. Alternatively,
the worst one also can be thought of as the unique solution to the minimization problem of the ex
ante expected payoffs.
3.2 The Neutral Bargaining Solution
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