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.

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
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Q3

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
(ii) Negotiation (Neg.).
(3.1)
or
Likewise, country U also has two strategies at its deposal, namely ,
(i) War
or
( ii) Negotiation (Neg.).
(3.2)
Finally, country A has two strategies at its deposal, namely,
(i)
Providing Assistance to Country U (Assist. ),
or (ii)
Staying Neutral ( Neutral ).
(3.3)
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 , YYY ),
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) ].
Transcribed Image Text: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 (ii) Negotiation (Neg.). (3.1) or Likewise, country U also has two strategies at its deposal, namely , (i) War or ( ii) Negotiation (Neg.). (3.2) Finally, country A has two strategies at its deposal, namely, (i) Providing Assistance to Country U (Assist. ), or (ii) Staying Neutral ( Neutral ). (3.3) 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 , YYY ), 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) ].
The payoff table for country A is given by
( War, War ) ( War , Neg. ) ( Neg. , War ) ( Neg., Neg. )
Assist.
+ 5
+ 2
+ 2
Neutral
- 5
- 3
In the above table, inside the round brackets
( AAA , BBB ),
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.
Transcribed Image Text:The payoff table for country A is given by ( War, War ) ( War , Neg. ) ( Neg. , War ) ( Neg., Neg. ) Assist. + 5 + 2 + 2 Neutral - 5 - 3 In the above table, inside the round brackets ( AAA , BBB ), 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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