This activity has 4 theorical and practical exercises for which you will have to describe
the representation of each proposed game and its solutions.
1. Consider the following game in strategic or normal form.
A2 B2 C2
A1 1,0 1,2 -2,1
B1 6,2 0,3 2,3
C1 2,2 -2,1 2,3
▸ Use the iterative elimination of strictly dominated strategies to reduce the game
as much as possible.
▸ What is the set of rationalizable strategies for each player?

Microeconomics (code ECO2023)
Actividades 2
© MIU City University Miami
▸ What is/are Nash equilibrium(s) in this game?
▸ Explain the differences between cooperative and non- cooperative games. What
are the fundamental hypotheses about the behavior of the persons in Game
theory?
2. Two hunters may choose, individually and simultaneously, to go deer hunting, as
the deer can provide abundant and appetizing food, or to go hare hunting, also
appetizing, but scarce. Deer hunting represents a challenge and requires mutual
coordination. Hunting a deer without cooperation means that the deer will be
safe; while hunting a deer in groups guarantees it will be caught. Hare hunting is
an individual activity that does not require another hunter, and the one who
decides to go hare hunting always makes it. The reward for hunting a hare is 1,
while the reward for each of the hunters for catching a deer together is 3 for each
one. The reward for not hunting a deer is 0.
▸ Specify the game in a normal way arising from this situation.
▸ Do the players have strictly dominated strategies? Determine the set of
rationalizable strategies in this case.
▸ Find all Nash equilibriums in this case, if any. Are they efficient in Pareto sense?
Justify your answer.
3. Marta and Sara are two students that devote part of their free time to doing
surveys for a market research company. The income obtained from this activity
depends on the number of surveys they do, bearing in mind that the girls may
freely choose the interviewees. As they both live in the same neighborhood in case,
they just interview their neighbors (N), they compete for the same people and
their monthly income is about 250 Euros. If they both choose to go to other
neighborhoods of the city and interview strangers (S), they can carry out more
surveys and both their incomes would be 400. If one of them decides to go and
interview people in another neighborhood but the other one does not, the former
will obtain income for 500, and the latter for 300, and vice versa. After receiving

Microeconomics (code ECO2023)
Actividades 3
© MIU City University Miami
the order from the company, Marta is always the one who starts to work first. Sara
has information about the places where Marta has done the surveys. Please:
▸ Represent this game extensively.
▸ Represent this game normally and look for Nash equilibrium.
▸ Calculate the perfect equilibrium in subgames.
▸ Now imagine that none of the girls can know where the other one is carrying out
the surveys (there is not sequentially). Represent the new game normally and
calculate Nash equilibrium(s) of the game.
4. Consider the following game in normal form.
Not cooperate Cooperate
Not cooperate 20,20 50,0
Cooperate 0,50 40,40
▸ What is Nash equilibrium? Is it efficient? Why?
▸ What needs to be complied with so that the players would like to cooperate? What
happens when one of the players does not cooperate? Why? Define trigger
strategy.
▸ Calculate the discount factor (δ) that would make both players decide to
cooperate.

Question

This activity has 4 theorical and practical exercises for which you will have to describe
the representation of each proposed game and its solutions.
1. Consider the following game in strategic or normal form.
A2 B2 C2
A1 1,0 1,2 -2,1
B1 6,2 0,3 2,3
C1 2,2 -2,1 2,3
▸ Use the iterative elimination of strictly dominated strategies to reduce the game
as much as possible.
▸ What is the set of rationalizable strategies for each player?

Microeconomics (code ECO2023)
Actividades 2
© MIU City University Miami
▸ What is/are Nash equilibrium(s) in this game?
▸ Explain the differences between cooperative and non- cooperative games. What
are the fundamental hypotheses about the behavior of the persons in Game
theory?
2. Two hunters may choose, individually and simultaneously, to go deer hunting, as
the deer can provide abundant and appetizing food, or to go hare hunting, also
appetizing, but scarce. Deer hunting represents a challenge and requires mutual
coordination. Hunting a deer without cooperation means that the deer will be
safe; while hunting a deer in groups guarantees it will be caught. Hare hunting is
an individual activity that does not require another hunter, and the one who
decides to go hare hunting always makes it. The reward for hunting a hare is 1,
while the reward for each of the hunters for catching a deer together is 3 for each
one. The reward for not hunting a deer is 0.
▸ Specify the game in a normal way arising from this situation.
▸ Do the players have strictly dominated strategies? Determine the set of
rationalizable strategies in this case.
▸ Find all Nash equilibriums in this case, if any. Are they efficient in Pareto sense?
Justify your answer.
3. Marta and Sara are two students that devote part of their free time to doing
surveys for a market research company. The income obtained from this activity
depends on the number of surveys they do, bearing in mind that the girls may
freely choose the interviewees. As they both live in the same neighborhood in case,
they just interview their neighbors (N), they compete for the same people and
their monthly income is about 250 Euros. If they both choose to go to other
neighborhoods of the city and interview strangers (S), they can carry out more
surveys and both their incomes would be 400. If one of them decides to go and
interview people in another neighborhood but the other one does not, the former
will obtain income for 500, and the latter for 300, and vice versa. After receiving

Microeconomics (code ECO2023)
Actividades 3
© MIU City University Miami
the order from the company, Marta is always the one who starts to work first. Sara
has information about the places where Marta has done the surveys. Please:
▸ Represent this game extensively.
▸ Represent this game normally and look for Nash equilibrium.
▸ Calculate the perfect equilibrium in subgames.
▸ Now imagine that none of the girls can know where the other one is carrying out
the surveys (there is not sequentially). Represent the new game normally and
calculate Nash equilibrium(s) of the game.
4. Consider the following game in normal form.
Not cooperate Cooperate
Not cooperate 20,20 50,0
Cooperate 0,50 40,40
▸ What is Nash equilibrium? Is it efficient? Why?
▸ What needs to be complied with so that the players would like to cooperate? What
happens when one of the players does not cooperate? Why? Define trigger
strategy.
▸ Calculate the discount factor (δ) that would make both players decide to
cooperate.

Accepted Answer

You have asked multiple questions in single question; hence provided solution for the first three…