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Bargaining Over Power: When Do Rapid Shifts in Power Lead to War?
Unformatted Document Text:  The evolution of capabilities in the model is dynamic, in the sense that today’s capabilities affect tomorrow’s. 6 For example, a weapons factory is itself a capability that can be used to produce weapons. As a result, the fact that the players do not exchange any capability does not imply that the distribution of capabilities is fixed over time: even if its capabilities are low now, a state might be able to secure more of them in the future. 7 This, in turn, enables the possibility of a rate of growth in the model, and hence lets us model situations in which commitment problems are likely to emerge. 8 4 The Model I analyze a stochastic model of sequential bargaining in which players bargain both over a pie and over capabilities. 9 Stochastic models, contrary to typical repeated games, have the advantage of being truly dynamic in the sense that current actions affect future states. 10 Here, the ability to influence the very nature of the game played in the next stage is crucial: to make their promises about the future credible, the players need to be able to influence today the payoff structure of the game they will play tomorrow. Thus, capabilities and the transfer thereof play a decisive role as the link between successive periods: by giving up capabilities now, the rising state is able to change his reservation point in the next period, thereby enabling commitment. Setup: Let Γ be a discounted stochastic game with T + 1 stages (t = 0, 1, . . . , T ; players to bargain over potential capabilities as well. For example, France demanded a high monetarycompensation from Germany in the aftermath of WWI to slow down its recovery. The only assumptionneeded is that the players have control over both their existing and latent capabilities. 6 They do so stochastically. Evidently, this does include the case of deterministic transition functions asspecial (degenerate) cases of this general class of bargaining situations. 7 In other words, we can very well have a sequence (c i1 , c i2 , c i3 , . . .) such that c it +1 > c it for all t, even if the players’ have not exchanged any capabilities 8 This is in contrast to Fearon (1996), where power only changes when the actors proceed to an exchangeof objects. 9 A stochastic game is “a repeated game where the state of nature may change from stage to stage,according to a lottery which, just like the current payoff, depends on current state and actions” (Mertens2002). 10 In fact, repeated games are only a special case of stochastic models, in which the initial stage gamehas a degenerate transition function (i.e., the initial state is absorbing), so that the same stage game isplayed over and over, regardless of the actors’ previous actions. 6

Authors: Chadefaux, Thomas.
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The evolution of capabilities in the model is dynamic, in the sense that today’s
capabilities affect tomorrow’s.
6
For example, a weapons factory is itself a capability that
can be used to produce weapons. As a result, the fact that the players do not exchange
any capability does not imply that the distribution of capabilities is fixed over time:
even if its capabilities are low now, a state might be able to secure more of them in the
future.
7
This, in turn, enables the possibility of a rate of growth in the model, and hence
lets us model situations in which commitment problems are likely to emerge.
8
4
The Model
I analyze a stochastic model of sequential bargaining in which players bargain both over
a pie and over capabilities.
9
Stochastic models, contrary to typical repeated games,
have the advantage of being truly dynamic in the sense that current actions affect future
states.
10
Here, the ability to influence the very nature of the game played in the next
stage is crucial: to make their promises about the future credible, the players need to be
able to influence today the payoff structure of the game they will play tomorrow. Thus,
capabilities and the transfer thereof play a decisive role as the link between successive
periods: by giving up capabilities now, the rising state is able to change his reservation
point in the next period, thereby enabling commitment.
Setup: Let Γ be a discounted stochastic game with T + 1 stages (t = 0, 1, . . . , T ;
players to bargain over potential capabilities as well. For example, France demanded a high monetary
compensation from Germany in the aftermath of WWI to slow down its recovery. The only assumption
needed is that the players have control over both their existing and latent capabilities.
6
They do so stochastically. Evidently, this does include the case of deterministic transition functions as
special (degenerate) cases of this general class of bargaining situations.
7
In other words, we can very well have a sequence (c
i
1
, c
i
2
, c
i
3
, . . .) such that c
i
t
+1
> c
i
t
for all t, even if the
players’ have not exchanged any capabilities
8
This is in contrast to Fearon (1996), where power only changes when the actors proceed to an exchange
of objects.
9
A stochastic game is “a repeated game where the state of nature may change from stage to stage,
according to a lottery which, just like the current payoff, depends on current state and actions” (Mertens
2002).
10
In fact, repeated games are only a special case of stochastic models, in which the initial stage game
has a degenerate transition function (i.e., the initial state is absorbing), so that the same stage game is
played over and over, regardless of the actors’ previous actions.
6


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