Lemma 5.4.

Let Γ

′′

be a game in which capabilities cannot be transferred, but the players

can negotiate over the timing of their negotiations i.e., Γ

′′

t

= (Γ

t

{Ω

t

}) ∪ {Ω

′′

t

}, where

Ω

′′

t

= x

t

,

∆

t

∈ R

2

: 0 ≤ x

t

≤ X and ∆

t

>

0 .

Then war occurs in equilibrium in stage Γ

′′

t

whenever M

i

t

>

max

σ

i

V

i

(σ|c

t

) − δM

j

t

.

Thus, the problem is for B to ﬁnd a way to commit not to exploit his stronger power

in the next period. B could try convincing A of his intentions, but this is essentially

cheap talk and is not credible, as B will have an incentive to renege on his promise in the

next period. Therefore, any credible mechanism of commitment must involve changing

B

’s incentives tomorrow. Proposition 5.1 ensures that this is always possible:

Proposition 5.1.

Eﬃciency: War never occurs in equilibrium in Γ

This result is important: it shows that the ineﬃciency condition derived in Powell

(2004) never holds when transfers of capabilities are added as a dimension in the

bargaining space. By giving up capabilities now, B changes his expected maximization

problem in the next period, and hence credible commits to the agreement in the next

period. Most important, the result holds no matter how rapidly power shifts. Note

moreover that the result is applicable to any bargaining protocol with an outside option.

As a result, fast changes in relative power associated with commitment problems cannot

be a suﬃcient explanation for war.

Obviously, B should only give up enough capabilities to keep A satisﬁed: below this

level, B’s future power remains too high and A prefers to ﬁght now. Beyond it, B gives

up too much and A will be tempted to ﬁght tomorrow. Proposition 5.1 ensures that

there always exists an amount of capabilities c

∗

for B to give up that falls between these

two bounds. The precise bounds of c

∗

are a function of the amount of the pie obtained

in the current period, and the minimum future power the player is willing to accept.

19

19

Note that the lemma only establishes bounds for the agreement. The speciﬁc agreement reached within

11