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Kim: Endogenous Choice of a Mediator
status quo mechanism, would the players both agree to switch to another mediator in some sequential
equilibrium, noting that information might be revealed by the players’ votes, which could affect
the continuation payoffs of the players?
Therefore, I must allow for the fact that if one of the players votes in favor and one votes against,
the players are going to learn from disagreement, consequently affecting their payoffs. I consider a
pairwise test in a ratification game where some uninformed third party can announce an alternative
mechanism and the players can switch. From the noncooperative approach, a reasonable restriction
on the selection of a mediator is that such a mediator should survive a vote against any alternative
options. Whether such a mediator exists is unclear, but if it does exist, we would have a compelling
reason to select it. The notion of survivability against all alternatives in a pairwise voting game will
be formalized as a concept of what I call threat-security. What I find in this context is that there
exists only one threat-secure mediator that will always survive the vote against any alternatives,
and it is the one that is ex ante Pareto dominated by any alternative mediator.
Equivalence of the Two Approaches
In both approaches, the selected mediator is not the
ex ante incentive efficient choice. Both approaches not only offer ex ante incentive inefficiency, but
also lead to the same inefficient mediator. That is, the threat-secure mediator is exactly the same
as the neutral bargaining solution. In general, the neutral bargaining solutions and the threatsecure
set are not nested. However, in the class of bargaining games I consider, two distinct ways
of looking at the problem lead to the same suboptimal choice of a mediator, which represents, of
all the interim incentive efficient mediators, the most ex ante inefficient 3 and the least peaceful
mediator, whereas the ex ante incentive efficient one is the most peaceful mediator. In this sense,
I argue that the process of selecting a mediator itself has an inherent inefficiency in bargaining.
The strategic intuition as to why the ex ante incentive efficient mediator does not survive
in the noncooperative game underscores the intuition behind the information leakage problem in
the cooperative game. In the cooperative sense, players pick a mediator, effectively pooling in a
way that reveals no information. But the nature of that pooling is exactly like signaling in the
noncooperative game. The novelty of this paper is that it provides a first attempt to connect a
cooperative bargaining theory 4 to a noncooperative ratification game.
3 Precisely stated, contrary to the ex ante incentive efficient mediator, the most ex ante inefficient mediator is
a solution to the program of minimizing the players’ ex ante expected payoffs over the set of all interim incentive
efficient mediators.
4 For classical bargaining literature, see Nash (1950), Nash (1953) (the canonical solution concept for two-person
bargaining problems), Harsanyi and Selten (1972) (an extension of the Nash bargaining solution for two-person games
with incomplete information), and Myerson (1979) (a modified version of Harsanyi and Selten (1972)).
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