1. You have a choice of getting a degree in economics, computer science or neither. Either degree decreases your future payoff by 5. After you make your choice, there is a 40% chance that economics degree is going to be in high demand, a 40% chance that a computer science degree is going to be in high demand, and a 20% chance that neither degree is going to be in high demand. If a degree is in high demand and you chose to get it, your payoff is 16. Getting a degree that is not in high demand provides you with a payoff of 9. Not getting a degree always provides you with a payoff of 5. a) What is the optimal choice for this problem? b) Provided you can obtain information about future demand for a de- gree, what is the maximum amount you are willing to pay for it? 2. Consider a variation of the Battle of the Sexes game with different payoffs. Players can either go to opera (0) or football (F). As usual, players only obtain non-zero payoffs if they pick the same option. If opera is chosen by both players, Player 1 obtains a payoff of 5 while Player 2 obtains the payoff of 2. If football is chosen by both players, Player 1 obtains a payoff of 2 while Player 2 obtains the payoff of 5. a) Write down both the normal-form and the matrix representation of this game. b) Find all pure strategy Nash-Equilibria. c) Find the unique mixed-strategy NE in which both players alternate between their pure strategies. 3. Given the following game in the matrix form: C R U 1,-1 | 2, 2 4, 4 M 2, -1 | 1, 0 |-2, 2 D 5, 3 0, 0 | 1, 1 L a) Find all NE.
1. You have a choice of getting a degree in economics, computer science or neither. Either degree decreases your future payoff by 5. After you make your choice, there is a 40% chance that economics degree is going to be in high demand, a 40% chance that a computer science degree is going to be in high demand, and a 20% chance that neither degree is going to be in high demand. If a degree is in high demand and you chose to get it, your payoff is 16. Getting a degree that is not in high demand provides you with a payoff of 9. Not getting a degree always provides you with a payoff of 5. a) What is the optimal choice for this problem? b) Provided you can obtain information about future demand for a de- gree, what is the maximum amount you are willing to pay for it? 2. Consider a variation of the Battle of the Sexes game with different payoffs. Players can either go to opera (0) or football (F). As usual, players only obtain non-zero payoffs if they pick the same option. If opera is chosen by both players, Player 1 obtains a payoff of 5 while Player 2 obtains the payoff of 2. If football is chosen by both players, Player 1 obtains a payoff of 2 while Player 2 obtains the payoff of 5. a) Write down both the normal-form and the matrix representation of this game. b) Find all pure strategy Nash-Equilibria. c) Find the unique mixed-strategy NE in which both players alternate between their pure strategies. 3. Given the following game in the matrix form: C R U 1,-1 | 2, 2 4, 4 M 2, -1 | 1, 0 |-2, 2 D 5, 3 0, 0 | 1, 1 L a) Find all NE.
Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.2P
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Transcribed Image Text:1. You have a choice of getting a degree in economics, computer science
or neither. Either degree decreases your future payoff by 5. After you make
your choice, there is a 40% chance that economics degree is going to be in
high demand, a 40% chance that a computer science degree is going to be in
high demand, and a 20% chance that neither degree is going to be in high
demand. If a degree is in high demand and you chose to get it, your payoff is
16. Getting a degree that is not in high demand provides you with a payoff
of 9. Not getting a degree always provides you with a payoff of 5.
a) What is the optimal choice for this problem?
b) Provided you can obtain information about future demand for a de-
gree, what is the maximum amount you are willing to pay for it?
2. Consider a variation of the Battle of the Sexes game with different
payoffs. Players can either go to opera (O) or football (F). As usual, players
only obtain non-zero payoffs if they pick the same option. If opera is chosen
by both players, Player 1 obtains a payoff of 5 while Player 2 obtains the
payoff of 2. If football is chosen by both players, Player 1 obtains a payoff of
2 while Player 2 obtains the payoff of 5.
a) Write down both the normal-form and the matrix representation of
this game.
b) Find all pure strategy Nash-Equilibria.
c) Find the unique mixed-strategy NE in which both players alternate
between their pure strategies.
3. Given the following game in the matrix form:
L CR
U 1, -1 | 2, 2 | 4, 4
М [2, -1| 1, 0 1-2, 2
D 5, 3 | 0, 0 | 1, 1
a) Find all NE.
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