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Kim: Endogenous Choice of a Mediator
vetoing, since the inequality in (T7) is satisfied with both sides equal to zero. Since (6.1)>(6.2),
player 1 of a strong type strictly benefits from the veto conditional on player 2 voting for µ 5/17,0 .
Thus, the strong type must always veto the change from µ 1,0 to an ex ante Pareto superior mediator
µ 5/17,0 .
In fact, the only credible vote belief for both players is ¯q·,i = (¯q i,i (s) = 1, ¯q −i,i (w) = 1) for all i.
That is, there exists a credible veto set V i = {s} for all i (and there is no other vote belief satisfying
(ii) of Definition 2) that can make the following speech:
“I voted against the alternative because my type is s. If you believe me and I am telling
you the truth, then my payoff in disagreement outcome G µ 1,0
is better than what I get
with the alternative. Moreover, if my type is w, I would get a higher payoff from the
alternative mediator than from G µ 1,0
in which you believe my type is s, and so I would
not want to vote against the alternative. Hence, you should believe me.”
The reasoning behind this example is also straightforward. With the alternative mediator µ 5/17,0 ,
the weak types gain by participating, but strong types lose. By vetoing the alternative, a player
sends a credible signal that he is of a strong type. Because a strong type gains relatively more by
disposing of mediator µ 1,0 and going to war for sure in the status quo, the other player responds
optimally by going to war less often after a veto, which in turn strengthens a vetoer’s incentive to
disclose his displeasure with the alternative. A strong type’s signal is credible because a weak type
does better with the alternative mediator.
If a veto resulted in passive inferences in this case, then the alternative µ 5/17,0 still should
not be ratifiable against µ 1,0 . If the inferences are required to satisfy the credibility conditions,
then the alternative is also not unanimously ratified by all types of all players, strengthening
the participation constraints even more, by improving the status quo payoffs for the vetoer. In
fact, iteratively performing a pairwise test between µ 1,0 and any other alternative, no alternative
mediator is ratifiable against µ 1,0 . Therefore, by Definition 5, µ 1,0 is threat-secure and is the only
threat-secure mediator among all interim incentive efficient mediators.
Figure 6.3 shows, for the range of ¯p(s), that the concept of threat-security picks out a unique
mediator from the set of interim incentive efficient mediators. Moreover, the threat-secure mediator
is indeed the same as the neutral bargaining solution.
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