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:  of u i (·), u B (1 − x ∗s ) = u B (1 − p s ) ≥ 1 − p s , and u A (x ∗s ) ≥ p s . Then, V A s (σ ∗ |c s ) ≥ δ s u A (x ∗s ) + V A n (σ|c n ) ≥ δ s p s + T t=n δ t (p n (E s [c n |c ∗s ]) − δ n l A > T t=s δ t p s − δ s l A since δ s > δ n = V A s (σ|c t ) By lemma 5.2, and V B s (σ ∗ |c s ) ≥ δ s u B (1 − x ∗s ) + V B n (σ|c n ) ≥ δ s [1 − p s ] + T t=n δ t (1 − p n (E s [c n |c ∗s ])]) − δ n l B > T t=s δ t (1 − p s ) − δ s l B = V B s (σ|c s ) Hence, there exists at least one strategy profile such that both players have an incentive to deviate from σ. But this contradicts the assumption that the use of the outside option was an equilibrium strategy. Proof of Lemma 5.5 I prove here the case where T = ∞. Clearly, a similar argument can be made by backward induction for T < ∞. Note first that we can define p n = β t p t without loss of generality. Then the whole 31

Authors: Chadefaux, Thomas.
first   previous   Page 33 of 45   next   last



background image
of u
i
(·), u
B
(1 − x

s
) = u
B
(1 − p
s
) ≥ 1 − p
s
, and u
A
(x

s
) ≥ p
s
. Then,
V
A
s
|c
s
) ≥ δ
s
u
A
(x

s
) + V
A
n
(σ|c
n
)
≥ δ
s
p
s
+
T
t=n
δ
t
(p
n
(E
s
[c
n
|c

s
]) − δ
n
l
A
>
T
t=s
δ
t
p
s
− δ
s
l
A
since δ
s
> δ
n
= V
A
s
(σ|c
t
)
By lemma 5.2,
and
V
B
s
|c
s
) ≥ δ
s
u
B
(1 − x

s
) + V
B
n
(σ|c
n
)
≥ δ
s
[1 − p
s
] +
T
t=n
δ
t
(1 − p
n
(E
s
[c
n
|c

s
])]) − δ
n
l
B
>
T
t=s
δ
t
(1 − p
s
) − δ
s
l
B
=
V
B
s
(σ|c
s
)
Hence, there exists at least one strategy profile such that both players have an
incentive to deviate from σ. But this contradicts the assumption that the use of the
outside option was an equilibrium strategy.
Proof of Lemma 5.5
I prove here the case where T = ∞. Clearly, a similar argument can be made by
backward induction for T < ∞.
Note first that we can define p
n
= β
t
p
t
without loss of generality. Then the whole
31


Convention
Submission, Review, and Scheduling! All Academic Convention can help with all of your abstract management needs and many more. Contact us today for a quote!
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 33 of 45   next   last

©2012 All Academic, Inc.