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