Homework 1 – Application to Game Theory
Question 1
a) This one describes strategic interaction, due to having at least 2 decision-makers of China and
the US both can decide which and in what degree they impose tariffs, which creates a new
decision to the other player.
b) This is again a strategic interaction, with a party nominee and at least one other competitor
who is campaigning for presidency. Choosing which financing to use, thus an impact on
whether the campaign of one player is successful.
c) This is an individual decision. Choosing whether to buy songs or whole albums just affects
oneself, where no interaction with others is needed or caused to do the purchase.
Question 2
a) a = 1
Cooperate Defect
Cooperate 72,72 64,64
Defect 64,64 36,36
We have C , C> C , D> D ,C > D , D and the Best Response of both players is to {cooperate}.
So, we have NO Prisoners´ Dilemma.
b) Now we have the condition that the Best Response of both players must be {defect}. So, we
have now a payoff order of:
D , C>C ,C > D , D>C , D
So, we have inequations of 54+ 10 a>36+36 a> 18+18 a>10+54 a
Solving these leads to:
54+ 10 a>36+36 a
18>26 a
9 /13> a
36+36 a>18+18 a
18>−18 a
−1<a
This is already clear due to the condition that a is a non-negative number (a>0)
18+18 a>10+ 54 a
8>36 a
2/9> a
So, to solve all equations a hold as: 2/9>a>0
Question 3
Help Not Help
Help 2,2 2,3
Not Help 3,2 0,0
The pure-strategy Nash equilibria are {not help ,help } and {help, not help }.
Question 1
a) This one describes strategic interaction, due to having at least 2 decision-makers of China and
the US both can decide which and in what degree they impose tariffs, which creates a new
decision to the other player.
b) This is again a strategic interaction, with a party nominee and at least one other competitor
who is campaigning for presidency. Choosing which financing to use, thus an impact on
whether the campaign of one player is successful.
c) This is an individual decision. Choosing whether to buy songs or whole albums just affects
oneself, where no interaction with others is needed or caused to do the purchase.
Question 2
a) a = 1
Cooperate Defect
Cooperate 72,72 64,64
Defect 64,64 36,36
We have C , C> C , D> D ,C > D , D and the Best Response of both players is to {cooperate}.
So, we have NO Prisoners´ Dilemma.
b) Now we have the condition that the Best Response of both players must be {defect}. So, we
have now a payoff order of:
D , C>C ,C > D , D>C , D
So, we have inequations of 54+ 10 a>36+36 a> 18+18 a>10+54 a
Solving these leads to:
54+ 10 a>36+36 a
18>26 a
9 /13> a
36+36 a>18+18 a
18>−18 a
−1<a
This is already clear due to the condition that a is a non-negative number (a>0)
18+18 a>10+ 54 a
8>36 a
2/9> a
So, to solve all equations a hold as: 2/9>a>0
Question 3
Help Not Help
Help 2,2 2,3
Not Help 3,2 0,0
The pure-strategy Nash equilibria are {not help ,help } and {help, not help }.
