DefinitionsConflict Model

Stability Analysis

Outline

2

Definitions

Normal Form Game vs. Relational Game

Relational Solution Concepts

3

The Graph Model of Conflict

4

Reachable List

5

Unilateral Improvement

6

Attitudes

7

Attitudes

8

Preference

Devoting Preference (DP)

Aggressive Preference (AP)

9

Relational Preference

10

Relational Preference

Total Relational Preference(TRP)

Total Relational Reply(TRR)

11

Set of Preferences

Normal Form Game

Relational Game

12

Nash Stability

Normal Form Game

Relational Game

13

Sequential Stability

Normal Form Game

Relational Game

14

General Meta Rationality

Normal Form Game

Relational Game

15

Symmetric Meta Rationality

Normal Form Game

Relational Game

16

The War of 1812

Conflict Model

17

The Americans declared war in 1812 for several

reasons, including:

trade restrictions brought about by Britain's ongoingwar with France

the impressment of American merchant sailors intothe Royal Navy

British support of American Indian tribes againstAmerican expansion

outrage over insults to national honor afterhumiliations on the high seas

History

18

The President of the United States

Admirals of the British Royal Navy

The British Prime Minister

Great Britain

Decision Makers

19

DM Options Feasible States

USA1. Declaration of War N Y N N Y N N Y N N Y N N Y N

2. Impose Trade Restrictions N N Y N N Y N N Y N N Y N N Y

GB

3.Repeal Impressment N N N Y Y Y N N N Y Y Y N N N

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

Feasible States

20

USA Moves

Graph Model

c

bam

on

g

ih

d

fe

j

lk21

GB Moves

Graph Model

d

j

a

m

g

22

GB Moves

Graph Model

e

k

b

n

h

23

Graph Model

f

l

c

o

i

24

GB Moves

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

Preference Vectors

25

Attitudes

USA GB

USA 0 -

GB - +

26

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

o m, n c, f, i, l

Reachable Lists

27

Stability Analysis

Normal Solution Concepts

Relational Solution Concepts

Misperceptions

28

Equilibrium X X X X X X E X X X X X X X X

USA Stability

Nash

SE

Q

Nash

SE

Q

Nash

SE

Q

Nash U

SE

Q U U U

Nash U U

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 U U U U U U U U

Nash 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 h

m o n

Normal Form Analysis

29

DM Options Feasible States

USA1. Declaration of War N Y N N Y N N Y N N Y N N Y N

2. Impose Trade Restrictions N N Y N N Y N N Y N N Y N N Y

GB

3.Repeal Impressment N N N Y Y Y N N N Y Y Y N N N

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

Feasible States

30

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

o GB GB 0

Normal Form Analysis

31

Equilibrium X X X X X X X X X X X E X E X

USA Stability

U U U U U U U U RN RN RN RN U RN U

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 StabilityRN 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 h

m o n

Relational Form Analysis

32

DM Options Feasible States

USA1. Declaration of War N Y N N Y N N Y N N Y N N Y N

2. Impose Trade Restrictions N N Y N N Y N N Y N N Y N N Y

GB

3.Repeal Impressment N N N Y Y Y N N N Y Y Y N N N

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

Feasible States

33

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

o GB GB GB GB 0

Relational Form Analysis

34

Attitudes in hyper game of the war of 1812

A First level hyper game

Hyper Game

USA GB

DMs USA GB DMs USA GB

USA 0 - USA + 0

GB - + GB 0 +

35

Equilibrium X X X X X X X X X X X E X X X

USA Stability

U U U U U U U U RN RN RN RN U RN U

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 StabilityRN 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 h

m o n

Overall Stability Analysis

36

DM Options Feasible States

USA1. Declaration of War N Y N N Y N N Y N N Y N N Y N

2. Impose Trade Restrictions N N Y N N Y N N Y N N Y N N Y

GB

3.Repeal Impressment N N N Y Y Y N N N Y Y Y N N N

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

Feasible States

37

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

Reference

38

Thank You for Your AttentionAny Question?

39