However, the incentives for both players are conditioned by the probability of leadership turnover,
which determines the value of information to the challenger and the defender’s incentives to mis-
represent it. First, with probability (1 − e), the informational problem in Stage 1 is recreated in
Stage 3 with the accession of a new leader; information gained in the previous stages is replaced
with new uncertainties. Second, the shadow of leadership turnover affects the defender’s incentives
to misrepresent private information; with a less certain future, the expected gains from bluffing are
reduced. These tensions produce seven propositions.
Proposition 1. The probability of conflict is greatest immediately following the accession of a new
leader and decreases over time.
This characterizes the primary skimming result. At each accession of a new leader, whether
in Stage 1 or in the D
2
branch of Stage 3, the challenger’s prior beliefs over the defender’s type
are given by θ
D
i
∼ U d, d . The challenger’s initial offer in Stage 1 takes into account its own
reservation value w
c
, the weakest defender type supported by its beliefs d, and the probability
e that D
1
survives to Stage 3. After observing the challenger’s offer, all defender types whose
reservation value d is greater than the offer x
1
, or for whom d > x
1
, reject. Among the types that
prefer the offer to rejecting it in the current period, or x
1
> d, some nonetheless reject, hoping that
current conflict payoffs will be outweighed by greater gains in the future. The cutpoint d
1
arises
endogenously from the tradeoff of future expectations, dividing these weak types into those who
accept and those who can afford to bluff in Stage 1.
d
1
=
2x
1
(8 + 6e + e
2
) + (w
c
− 1)(4 + 6e + e
2
)
12 + 6e + e
2
(1)
Those types defined by [d, d
1
] accept, while types in the range d
1
, d reject, opening up the
possibility of conflict. The probability of conflict at Stage 1 is the probability that, conditional on
18
Convention