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:  M i t , with strict equality for at least one i ∈ {A, B}. V A (σ ∗ |ω ∗ t , c ∗t ) ≥ δ t u (p t + ǫ) + T r=t+∆ ∗ t δ r [(1 − ∆ ∗t )p t + ∆ ∗t (λp n )] − δ (t+∆ ∗ t ) l A ≥ δ t p t − δ (t+∆ ∗ t ) l A + δ t ǫ + T r=t+∆ ∗ t δ r [p t − ∆ ∗t p t + ∆ ∗t λp n ] > M A t + δ t ǫ − ∆ ∗t T r=t+∆ ∗ t δ r p t + ∆ ∗t λ T r=t+∆ ∗ t δ r p n , since δ (t+∆ ∗ t ) < δ t = M A t + δ t ǫ − δ t ǫ Tr=n δ r (p t − λp n ) × T r=t+∆ ∗ t δ r (p t − λp n ) > M A t since T r=n δ r < T r=t+∆ ∗ t δ r Let us now see that B would weakly prefer this agreement to fighting. First, note that (1 − p t − ǫ ) > 0, since ǫ < (1 − p t ) and p t < 1, and hence u(1 − p t − ǫ ) > 1 − p t − ǫ . Then B’s payoff is: V B (σ ∗ |ω ∗ t , c ∗t ) ≥ δ t u (1 − p t − ǫ) + T r=t+∆ ∗ t δ r 1 − (1 − ∆ ∗t )p t + ∆ ∗t (p n ) − δ (t+∆ ∗ t ) l B ≥ δ t (1 − p t − ǫ) + T r=t+∆ ∗ t δ r 1 − p t + ∆ ∗t p t + ∆ ∗t p n − δ (t+∆ ∗ t ) l B ≥ T r=t δ r (1 − p t ) − δ (t+∆ ∗ t ) l B − δ t ǫ + ∆ ∗t T r=t+∆ ∗ t δ r (p t − p n ) ≥ M B t + δ t l B 1 − δ ∆ ∗ t − δ t ǫ since p n = p t , and δ (t+∆ ∗ t ) l B < δ t l B ≥ M B t since ǫ ≤ l B 1 − δ ∆ ∗ t by assumption Hence, there exists at least one agreement ω ∗ t ∈ Ω such that at least one player has an incentive to deviate. 35

Authors: Chadefaux, Thomas.
first   previous   Page 37 of 45   next   last



background image
M
i
t
, with strict equality for at least one i ∈ {A, B}.
V
A
t
, c

t
) ≥ δ
t
u
(p
t
+ ǫ) +
T
r=t+∆
t
δ
r
[(1 − ∆

t
)p
t
+ ∆

t
(λp
n
)] − δ
(t+∆
t
)
l
A
≥ δ
t
p
t
− δ
(t+∆
t
)
l
A
+ δ
t
ǫ
+
T
r=t+∆
t
δ
r
[p
t
− ∆

t
p
t
+ ∆

t
λp
n
]
> M
A
t
+ δ
t
ǫ
− ∆

t
T
r=t+∆
t
δ
r
p
t
+ ∆

t
λ
T
r=t+∆
t
δ
r
p
n
,
since δ
(t+∆
t
)
< δ
t
= M
A
t
+ δ
t
ǫ
δ
t
ǫ
T
r=n
δ
r
(p
t
− λp
n
)
×
T
r=t+∆
t
δ
r
(p
t
− λp
n
)
> M
A
t
since
T
r=n
δ
r
<
T
r=t+∆
t
δ
r
Let us now see that B would weakly prefer this agreement to fighting. First, note
that (1 − p
t
− ǫ
) > 0, since ǫ < (1 − p
t
) and p
t
<
1, and hence u(1 − p
t
− ǫ
) > 1 − p
t
− ǫ
.
Then B’s payoff is:
V
B
t
, c

t
) ≥ δ
t
u
(1 − p
t
− ǫ) +
T
r=t+∆
t
δ
r
1 − (1 − ∆

t
)p
t
+ ∆

t
(p
n
)
− δ
(t+∆
t
)
l
B
≥ δ
t
(1 − p
t
− ǫ) +
T
r=t+∆
t
δ
r
1 − p
t
+ ∆

t
p
t
+ ∆

t
p
n
− δ
(t+∆
t
)
l
B
T
r=t
δ
r
(1 − p
t
) − δ
(t+∆
t
)
l
B
− δ
t
ǫ
+ ∆

t
T
r=t+∆
t
δ
r
(p
t
− p
n
)
≥ M
B
t
+ δ
t
l
B
1 − δ
t
− δ
t
ǫ
since p
n
= p
t
, and δ
(t+∆
t
)
l
B
< δ
t
l
B
≥ M
B
t
since ǫ ≤ l
B
1 − δ
t
by assumption
Hence, there exists at least one agreement ω
t
∈ Ω such that at least one player has
an incentive to deviate.
35


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 37 of 45   next   last

©2012 All Academic, Inc.