All Academic, Inc. Research Logo

Info/CitationFAQResearchAll Academic Inc.
Document

Bargaining Over Power: When Do Rapid Shifts in Power Lead to War?
Unformatted Document Text:  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 ] = Nn=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 in |c it ] =   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 i0 is exogenously defined. 12 This is without loss of generality, since only relative capabilities matter: by the monotonicity of p(c it ) (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

Authors: Chadefaux, Thomas.
first   previous   Page 9 of 45   next   last



background image
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


Convention
Convention is an application service for managing large or small academic conferences, annual meetings, and other types of events!
Submission - Custom fields, multiple submission types, tracks, audio visual, multiple upload formats, automatic conversion to pdf.
Review - Peer Review, Bulk reviewer assignment, bulk emails, ranking, z-score statistics, and multiple worksheets!
Reports - Many standard and custom reports generated while you wait. Print programs with participant indexes, event grids, and more!
Scheduling - Flexible and convenient grid scheduling within rooms and buildings. Conflict checking and advanced filtering.
Communication - Bulk email tools to help your administrators send reminders and responses. Use form letters, a message center, and much more!
Management - Search tools, duplicate people management, editing tools, submission transfers, many tools to manage a variety of conference management headaches!
Click here for more information.

first   previous   Page 9 of 45   next   last

©2012 All Academic, Inc.