1 ≤ T ≤ ∞), in which two players indexed by i ∈ {A, B} bargain over the partition of

both a ﬂow of beneﬁts X with size 1 and of a set of capabilities with size C > 0. In each

stage Γ

t

, the state variable c

i

t

captures player i’s share of capabilities and summarizes

the whole history of growth up to this point.

11

For simplicity, c

A

t

and c

B

t

are normalized

for all t so that c

A

t

+ c

B

t

= C in each period, while keeping their ratio unchanged.

12

Transition: The evolution of c

i

t

follows a general stochastic process, where q(c

i

n

|c

i

t

)+ε

n

is the probability that the distribution of capabilities in the next stage is c

i

n

, given that

it is c

i

t

today (ε

n

is an exogenous shock—a random variable with mean zero). Thus,

for N possible states, E

t

[c

i

n

|c

i

t

] =

N

n=1

q

(c

i

n

|c

i

t

)c

i

n

is A’s expected amount of capabilities

in the next period given that it is c

i

t

today.

13

E

t

[c

i

n

|c

i

t

] is assumed to be a continuous

and monotonically increasing function of c

i

t

, where the expectation is based on what is

known at time t. Moreover, I assume that c

i

t

= 0 and c

i

t

= C are two absorbing states

of the temporally homogeneous Markov process, which implies that:

E

t

[c

i

n

|c

i

t

] =

0

if c

i

t

= 0

0 < c

i

n

<

1 if 0 < c

i

t

< C

C

if c

i

t

= C

This is intuitive: a country without any capability (not even latent ones) cannot

create new ones. Together, these assumptions imply that tomorrow’s expected share

of capabilities can be set to any value in the interval [0, C] by transfers of capabilities

from one country to the other.

14

Indirectly, this also means that a player can reduce his

expected future power as much as necessary by transfers of capabilities today.

Agreement: Both players observe the current state and negotiate an agreement on

the partition of the pie X and the set of capabilities C. An agreement in stage Γ

t

is

11

I assume that the initial distribution of capabilities, c

i

0

is exogenously deﬁned.

12

This is without loss of generality, since only relative capabilities matter: by the monotonicity of p(c

i

t

)

(see below), burning x capabilities is equivalent to conceding an amount y

≤ x to the opponent.

13

The ﬁniteness of the number of states is without loss of generality.

14

Since E

t

[c

n

] is continuous on a closed interval [0, C], the intermediate value theorem applies: for all

y

∈ [0, C], there exists c

t

∈ C such that E

t

[c

n

|c

t

] = y.

7