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Kim: Endogenous Choice of a Mediator
Definition 2. (v, σ, ψ, ¯q) is an equilibrium ratification of γ when the status quo is G δ , if and only
if γ satisfies the conditions (T1) – (T3) and for all i either
(i) there does not exist a credible veto belief, or
(ii) for every credible vote belief ¯q·,i such that the conditions (T4) – (T9) are all satisfied,
∑
¯q −i,i (t −i ) ∑ γ(d|t)u i (d, t) = ∑ ¯q −i,i (t −i ){ψ i,i (t i )u i (d 0 , t)
d∈D
t −i
t −i
+ (1 − ψ i,i (t i )) · (ψ −i,i (t −i )u i (d 0 , t)
+ (1 − ψ −i,i (t −i )) ∑ σ i (r|t) ∑ δ(d|r)u i (d, t))}, ∀t i ∈ V i .
r∈R d∈D
Definition 3. An alternative mediator γ is ratifiable against the mediator δ if and only if there
exists an equilibrium ratification of γ when the status quo is G δ .
An alternative mediator γ is ratifiable against the mediator δ if and only if there exists a
sequential equilibrium of the two-stage game in which γ is unanimously voted for at every profile
of types, where beliefs following disagreement are required to satisfy the credibility conditions. If
after a veto, the players’ beliefs are restricted to credible vote beliefs, then the alternative mediator
is ratifiable.
An alternative mediator γ is not ratifiable against δ if and only if, for every equilibrium of the
two-stage ratification game, there exists a profile of types in which γ is not unanimously approved
over δ. That is, there is no equilibrium to the two-stage game in which γ is unanimously approved
over δ along every equilibrium path. The equation in (ii) of Definition 2 says that if for every
credible vote belief there is some type t i that strictly gains by vetoing, then γ is not ratifiable
relative to δ. This definition suggests that rejection of γ is not so severe. Given the definition of a
ratifiable alternative mediator, I can now define a secure status quo mechanism and a threat-secure
mediator.
Definition 4. A status quo mechanism G δ is secure if and only if every interim incentive efficient
mediator that is ratifiable against δ is an equilibrium of G δ under the prior beliefs.
A secure mechanism cannot be overturned by a ratifiable alternative. Moreover, if δ is ratifiable
against itself, then such a status quo mechanism G δ is not vulnerable to allowing players to send
preplay cheap talk messages that might communicate information about their types.
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