2. Outline

Conflict Stability
Definitions
Model Analysis
2

3. Definitions

Normal Form Game vs. Relational Game
Relational Solution Concepts
3

4. The Graph Model of Conflict


4

5. Reachable List


5

6. Unilateral Improvement


6

7. Attitudes


7

8. Attitudes


8

9. Preference

Devoting Preference (DP) Aggressive Preference (AP)
 
9

10. Relational Preference


10

11. Relational Preference

Total Relational Preference Total Relational Reply
(TRP) (TRR)
 
11

12. Set of Preferences

Normal Form Game Relational Game
 
12

13. Nash Stability

Normal Form Game Relational Game
 
13

14. Sequential Stability

Normal Form Game Relational Game
 
14

15. General Meta Rationality

Normal Form Game Relational Game
 
15

16. Symmetric Meta Rationality

Normal Form Game Relational Game
 
16

17. The War of 1812

Conflict Model
17

18. History

 The Americans declared war in 1812 for several
reasons, including:
 trade restrictions brought about by Britain's ongoing
war with France
 the impressment of American merchant sailors into
the Royal Navy
 British support of American Indian tribes against
American expansion
 outrage over insults to national honor after
humiliations on the high seas
18

19. Decision Makers

The President of the United States
Admirals of the British Royal Navy
The British Prime Minister
Great Britain
19

20. Feasible States

DM Options Feasible States
1. Declaration of War N Y N N Y N N Y N N Y N N Y N
USA
2. Impose Trade Restrictions N N Y N N Y N N Y N N Y N N Y
3.Repeal Impressment N N N Y Y Y N N N Y Y Y N N N
GB 4.Repeal Orders of Council N N N N N N Y Y Y Y Y Y N N N
5.Escalate Conflict N N N N N N N N N N N N Y Y Y
Label a b c d e f g h i j k l m n o
20

21. Graph Model

 USA Moves
c g
a b h i m
d j
n o
e f k l 21

22. Graph Model

 GB Moves
d a
g
j m
22

23. Graph Model

 GB Moves
e b
h
k n
23

24. Graph Model

 GB Moves
f c
i
l o
24

25. Preference Vectors

DMs Ordering of States from Most to Least Preferred
USA j l d f g i c a k e h b m n o
GB a c d f g i m o j l b e h n k
25

26. Attitudes


USA GB
USA 0 -
GB - +
26

27. Reachable Lists
State 
a b, c d, g, j, m
b a, c e, h, k, n
c a, b f, i, l, o
d e, f a, g, j, m
e d, f b, h, k, n
f d, e c, i, l, o
g h, i a, d, j, m
h g, i b, e, k, n
i g, h c, f, l, o
j k, l a, d, g, m
k j, l b, e, h, n
l j, k c, f, i, o
m n, o a, d, g, j
n m, o b, e, h, k 27
o m, n c, f, i, l

28. Stability Analysis

Normal Solution Concepts
Relational Solution Concepts
Misperceptions
28

29. Normal Form Analysis
Equilibrium X
X X X X X E X X X X X X X X
USA
Nash
Nash
Nash
Nash
Nash
SEQ
SEQ
SEQ
SEQ
U U U U U U
Stability
USA j l d f g i c a k e h b m n o
j d g c j d g c m m
l f i a n
GB Stability
Nash
Nash
Nash
U U U U U U U U U U U U
GB a c d f g i m o j l b e h n k
a c a c a c a c b b b b
d f d d f e e e
g g i h 29 h
m o n

30. Feasible States

DM Options Feasible States
1. Declaration of War N Y N N Y N N Y N N Y N N Y N
USA
2. Impose Trade Restrictions N N Y N N Y N N Y N N Y N N Y
3.Repeal Impressment N N N Y Y Y N N N Y Y Y N N N
GB 4.Repeal Orders of Council N N N N N N Y Y Y Y Y Y N N N
5.Escalate Conflict N N N N N N N N N N N N Y Y Y
Label a b c d e f g h i j k l m n o
30

31. Normal Form Analysis
Nash  SEQ SMR GMR # of EQ
a GB GB, USA GB, USA 2
b GB GB, USA GB, USA 2
c GB, USA GB, USA GB, USA GB, USA 4
d USA USA USA GB, USA 1
e USA 0
f USA GB, USA GB, USA 2
g USA USA USA, GB USA, GB 2
h GB, USA 1
i USA USA, GB GB, USA 2
j USA USA GB, USA GB, USA 2
k USA USA USA 0
l USA USA, GB USA, GB 2
m USA USA GB GB 0
n 0 31
o GB GB 0

32. Relational Form Analysis
Equilibrium X
 X X X X X X X X X X E X E X
USA
U U U U U U U U RN RN RN RN U RN U
Stability
USA j l d f g i c a k e h b m n o
k k e e h i b c n n
l f i h b o
GB Stability
RN RN U U U U RN RN U U RN U U RN U
GB a c d f g i m o j l b e h n k
a c a c a c b b b
d f e
g i 32 h
m o n

33. Feasible States

DM Options Feasible States
1. Declaration of War N Y N N Y N N Y N N Y N N Y N
USA
2. Impose Trade Restrictions N N Y N N Y N N Y N N Y N N Y
3.Repeal Impressment N N N Y Y Y N N N Y Y Y N N N
GB 4.Repeal Orders of Council N N N N N N Y Y Y Y Y Y N N N
5.Escalate Conflict N N N N N N N N N N N N Y Y Y
Label a b c d e f g h i j k l m n o
33

34. Relational Form Analysis
RNash  RSEQ RSMR RGMR # of EQ
a GB GB GB GB 0
b GB, USA GB, USA GB, USA GB, USA 4
c GB GB GB GB 0
d 0
e USA USA USA USA 0
f 0
g 0
h USA USA USA USA 0
i 0
j 0
k USA USA USA USA 0
l USA USA USA 0
m GB GB GB GB 0
n GB, USA GB, USA GB, USA GB, USA 4 34
o GB GB GB GB 0

35. Hyper Game

 Attitudes in hyper game of the war of 1812
USA GB
DMs USA GB DMs USA GB
USA 0 - USA + 0
GB - + GB 0 +
 A First level hyper game
35

36. Overall Stability Analysis
Equilibrium X
X X X X X X X X X X E X X X
USA
U U U U U U U U RN RN RN RN U RN U
Stability
USA j l d f g i c a k e h b m n o
k k e e h i b c n n
l f i h b o
GB Stability
RN RN U U U U U U U U RN U U U U
GB a c d f g i m o j l b e h n k
a c a c a c a c b b b b
d f d d f e e e
g g i h 36 h
m o n

37. Feasible States

DM Options Feasible States
1. Declaration of War N Y N N Y N N Y N N Y N N Y N
USA
2. Impose Trade Restrictions N N Y N N Y N N Y N N Y N N Y
3.Repeal Impressment N N N Y Y Y N N N Y Y Y N N N
GB 4.Repeal Orders of Council N N N N N N Y Y Y Y Y Y N N N
5.Escalate Conflict N N N N N N N N N N N N Y Y Y
Label a b c d e f g h i j k l m n o
37

38. Reference

Conflict Analysis Approaches for
Investigating Attitudes and Misperceptions in
the War of 1812
Takehiro INOHARA
Keith W. HIPEL
Sean WALKER
Journal of system science and system engineering, 2007
38

39. Thank You for Your Attention
Any Question?
39