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Kim: Endogenous Choice of a Mediator
A mediation mechanism µ is individually rational if and only if it satisfies the following participation
constraints:
U i (µ|t i ) ≥
∑
t −i ∈T −i
p i (t −i |t i )u i (d 0 , t), ∀i ∈ N, ∀t i ∈ T i .
Since the disagreement payments are normalized such that u i (d 0 , t) = 0 for all i and all t, the
participation constraints reduce to
U i (µ|t i ) ≥ 0, ∀i ∈ N, ∀t i ∈ T i .
The revelation principle (Myerson, 1979) implies that a mechanism cannot be implemented
by any equilibrium of a communication game induced by any communication system unless the
mechanism is incentive compatible and individually rational. Thus, there is no loss of generality in
focusing on such direct revelation mechanisms. 8
Therefore, taking relevant incentive constraints into account, I define the incentive feasible mediator
to be whoever mediates according to the incentive compatible, individually rational mediation
mechanism for the above Bayesian bargaining problem. That is, by the revelation principle, I
can naturally assume that players bargain over the set of incentive feasible mediators, denoted as
F . As I take a mediator to be synonymous with a mechanism, I use the terms mediator and its
corresponding mediation mechanism interchangeably throughout the paper.
2.2 The Benchmark Model
In this subsection, I consider the context of international relations in which two symmetric players,
each with two discrete types, must make a decision d ∈ D. For example, two states are involved
in a dispute over a divisible item, area of territory, or an allocation of resources that could lead to
war.
There are two possible decisions called d 0 and d 1 . Let D = {d 0 , d 1 }, where d 0 can be interpreted
as going to war, and d 1 as peace (e.g., negotiated settlement). Each i = {1, 2} has private information
t i ∈ T i = {s, w}, where s denotes the strong type and w denotes the weak type. I assume
that the types are independent; that is, t i is drawn from the distribution ¯p i independent of t −i ,
and this is common knowledge. For the sake of simplicity and tractability, I assume symmetry in
probability – that the prior marginal probability of the strong types are the same for both players;
8 See Holmström and Myerson (1983, 1804) and Myerson (1991, 487).
8