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Bargaining Over Power: When Do Rapid Shifts in Power Lead to War?
Unformatted Document Text:  [FIGURE 2 ABOUT HERE] Figure 2 is a graphical proof of the result: with fixed renegotiation times (at t 0 and t 1 ), A demands a concession of ˆ c now, which she believes will lead to c ∗ at time t 1 . If her misperception is too important, ˆ c might exceed what B is willing to give. However, there exist ˜ c and ∆ such that an agreement on ˜ c now would lead to an expected distribution of capabilities (given A’s beliefs) of c ∗ at time t ∆ . Hence, A is willing not to fight now, and to wait until t ∆ . Repeating the process until t 1 , then, allows both actors to avoid fighting. Thus, neither the extent of A’s misperception (λ), nor the speed at which relative power changes lead bargaining to break down. This result is robust to a wide variety of situations: First, note that B need not even know θ A or its probability distribution for the result to hold. In fact, it is easy to see that A has no incentive to misrepresent her beliefs, since such misrepresentation would only affect the frequency of negotiation (∆ t ), and not the distribution of capabilities and benefits. Hence A can credibly convey her beliefs to B. Moreover, it is easy to extend the analysis to two-sided uncertainty, or even to the case where B himself is uncertain about his own growth rate. 7 The Issue of Separability I have so far explicitly assumed that capabilities and benefits can be distinguished. That is, an object can be qualified either as a ‘capability’ or as a ‘benefit’, but not both. Yet, while it is reasonable to assume that states do not derive any direct utility from the possession of cannons, other objects such as territory play a double role: on the one hand, a larger territory increases space for the population, allows additional crops, generates economies of scale, etc. On the other hand, it is also a defensive capability (Levy 1984), or a source of raw materials. Even more problematic is the case of money, which is perfectly fungible into either benefits or military power. In fact, it is difficult 16

Authors: Chadefaux, Thomas.
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background image
[FIGURE 2 ABOUT HERE]
Figure 2 is a graphical proof of the result: with fixed renegotiation times (at t
0
and
t
1
), A demands a concession of ˆ
c
now, which she believes will lead to c
at time t
1
. If her
misperception is too important, ˆ
c
might exceed what B is willing to give. However, there
exist ˜
c
and ∆ such that an agreement on ˜
c
now would lead to an expected distribution
of capabilities (given A’s beliefs) of c
at time t
. Hence, A is willing not to fight now,
and to wait until t
. Repeating the process until t
1
, then, allows both actors to avoid
fighting. Thus, neither the extent of A’s misperception (λ), nor the speed at which
relative power changes lead bargaining to break down.
This result is robust to a wide variety of situations: First, note that B need not even
know θ
A
or its probability distribution for the result to hold. In fact, it is easy to see
that A has no incentive to misrepresent her beliefs, since such misrepresentation would
only affect the frequency of negotiation (∆
t
), and not the distribution of capabilities and
benefits. Hence A can credibly convey her beliefs to B. Moreover, it is easy to extend
the analysis to two-sided uncertainty, or even to the case where B himself is uncertain
about his own growth rate.
7
The Issue of Separability
I have so far explicitly assumed that capabilities and benefits can be distinguished.
That is, an object can be qualified either as a ‘capability’ or as a ‘benefit’, but not both.
Yet, while it is reasonable to assume that states do not derive any direct utility from
the possession of cannons, other objects such as territory play a double role: on the
one hand, a larger territory increases space for the population, allows additional crops,
generates economies of scale, etc. On the other hand, it is also a defensive capability
(Levy 1984), or a source of raw materials. Even more problematic is the case of money,
which is perfectly fungible into either benefits or military power. In fact, it is difficult
16


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