Answered: Question 3 Consider a hypothetical… | bartleby

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 28EQ

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Question 3
Consider a hypothetical conflict between countries R and U, involving a third
country A. Country R has two strategies at its deposal, namely,
(i) War
or
( ii) Negotiation (Neg.).
(3.1)
Likewise, country U also has two strategies at its deposal, namely,
(i) War
( ii) Negotiation (Neg.).
(3.2)
or
Finally, country A has two strategies at its deposal, namely,
(i)
Providing Assistance to Country U (Assist. ),
( ii)
Staying Neutral (Neutral ).
( 3.3)
or
The payoff table for country R is given by
( War, Assist. )(War, Neutral ) ( Neg. , Assist. ) ( Neg., Neutral )
War
- 10
+ 5
+ 8
+ 10
Neg.
- 5
+ 2
In the above table, inside the round brackets
(XXX, ҮҮҮ),
XXX represents the strategy applied by country U [refer to (3.2) ], and YYY
represents the strategy applied by country A [refer to (3.3)].
The payoff table for country U is given by
( War, Assist. ) ( War, Neutral ) (Neg., Assist. ) ( Neg.
Neutral)
War
- 10
- 20
+ 3
- 5
Neg.
- 20
- 30
+ 1
- 2
In the above table, inside the round brackets
( UUU , VVV ),
UUU represents the strategy applied by country R [refer to (3.1) ], and VVV
represents the strategy applied by country A [refer to (3.3)].
Q. 3 continues on the nert page

[ Question 3 continues...]
The payoff table for country A is given by
( War, War) ( War, Neg. ) ( Neg. , War ) ( Neg., Neg. )
Assist.
+ 5
0.
+ 2
+ 2
Neutral
- 5
3
In the above table, inside the round brackets
(АА , ВВB),
AAA represents the strategy applied by country R [refer to (3.1) ], and BBB
represents the strategy applied by country U [ refer to (3.2) ].
Does the game has any Nash equilibrium ? If your answer is "Yes", then you are
required to identify all the Nash equilibrium (equilibria ). Justify you answer.

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