A and B are a couple and they want to go into a concert. A comes from Bonn and loves the music of Ludwig van Beethoven. B comes from Salzburg and loves the music of Wolfgang Amadeus Mozart. There are two concerts in town: one with the music of Beethoven and one with the music of Mozart. Both (A and B) prefer to go to a concert together. If both go to a concert of Beethoven, A has a pay-off of 4 and B has a pay-off of 2. If both go to a concert of Mozart, B has a pay-off of 4 and A has a pay-off of 2. If A goes to a concert of Mozart and B to a concert of Beethoven, they are both miserable and get a pay-off of 0. But, if B goes to a concert of Mozart and A to a concert of Beethoven, they are both a little better off with a pay-off of 1. Both A and B have to make a simultaneous decision and cannot communicate prior to the decision. (a) Construct the pay-off matrix for this game. (b) Identify the Nash equilibrium or equilibria of the game. (c) Which off the allocations are pareto-efficient. Explain briefly why.
A and B are a couple and they want to go into a concert. A comes from Bonn and loves the music of Ludwig van Beethoven. B comes from Salzburg and loves the music of Wolfgang Amadeus Mozart. There are two concerts in town: one with the music of Beethoven and one with the music of Mozart. Both (A and B) prefer to go to a concert together. If both go to a concert of Beethoven, A has a pay-off of 4 and B has a pay-off of 2. If both go to a concert of Mozart, B has a pay-off of 4 and A has a pay-off of 2. If A goes to a concert of Mozart and B to a concert of Beethoven, they are both miserable and get a pay-off of 0. But, if B goes to a concert of Mozart and A to a concert of Beethoven, they are both a little better off with a pay-off of 1. Both A and B have to make a simultaneous decision and cannot communicate prior to the decision. (a) Construct the pay-off matrix for this game. (b) Identify the Nash equilibrium or equilibria of the game. (c) Which off the allocations are pareto-efficient. Explain briefly why.
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.5P
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Question
![A and B are a couple and they want to go into a concert. A comes from Bonn and
loves the music of Ludwig van Beethoven. B comes from Salzburg and loves the music
of Wolfgang Amadeus Mozart. There are two concerts in town: one with the music
of Beethoven and one with the music of Mozart. Both (A and B) prefer to go to a
concert together. If both go to a concert of Beethoven, A has a pay-off of 4 and B
has a pay-off of 2. If both go to a concert of Mozart, B has a pay-off of 4 and A has a
pay-off of 2. If A goes to a concert of Mozart and B to a concert of Beethoven, they
are both miserable and get a pay-off of 0. But, if B goes to a concert of Mozart and
A to a concert of Beethoven, they are both a little better off with a pay-off of 1.
Both A and B have to make a simultaneous decision and cannot communicate prior
to the decision.
(a)
Construct the pay-off matrix for this game.
(b)
Identify the Nash equilibrium or equilibria of the game.
(c)
Which off the allocations are pareto-efficient. Explain briefly why.
(d)
her own (i.e., one pay-off-point for B gives her more utility than one pay-off-
point for herself). Does this change the outcome of the game. If yes, explain why.
If not, explain why not.
Imagine now, A is altruistic and values the pay-off of B more than](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc5b12c3-3bda-4584-85a8-4ccf2fff5da3%2Ff15afa4b-d166-482b-9203-613103f8261f%2Fvthg44s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A and B are a couple and they want to go into a concert. A comes from Bonn and
loves the music of Ludwig van Beethoven. B comes from Salzburg and loves the music
of Wolfgang Amadeus Mozart. There are two concerts in town: one with the music
of Beethoven and one with the music of Mozart. Both (A and B) prefer to go to a
concert together. If both go to a concert of Beethoven, A has a pay-off of 4 and B
has a pay-off of 2. If both go to a concert of Mozart, B has a pay-off of 4 and A has a
pay-off of 2. If A goes to a concert of Mozart and B to a concert of Beethoven, they
are both miserable and get a pay-off of 0. But, if B goes to a concert of Mozart and
A to a concert of Beethoven, they are both a little better off with a pay-off of 1.
Both A and B have to make a simultaneous decision and cannot communicate prior
to the decision.
(a)
Construct the pay-off matrix for this game.
(b)
Identify the Nash equilibrium or equilibria of the game.
(c)
Which off the allocations are pareto-efficient. Explain briefly why.
(d)
her own (i.e., one pay-off-point for B gives her more utility than one pay-off-
point for herself). Does this change the outcome of the game. If yes, explain why.
If not, explain why not.
Imagine now, A is altruistic and values the pay-off of B more than
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