(a) Stan and Ollie are two students who share a flat. Both of them prefer to liıve in à clean Ilal. However, neither is too fond of housecleaning. Each of them receives a payoff of 12 if they both clean the flat. If neither person cleans the flat, they receive a payoff of 6 each. If one person cleans the flat but the other person does not, then the payoff for the person who does the cleaning is 5 and the payoff for the person who doesn't do any cleaning is 15. (i) Write down the payoff matrix of this game. Derive the dominant strategy equilibrium. Is this also a Nash equilibrium? (ii) Expiain your reasoning.
(a) Stan and Ollie are two students who share a flat. Both of them prefer to liıve in à clean Ilal. However, neither is too fond of housecleaning. Each of them receives a payoff of 12 if they both clean the flat. If neither person cleans the flat, they receive a payoff of 6 each. If one person cleans the flat but the other person does not, then the payoff for the person who does the cleaning is 5 and the payoff for the person who doesn't do any cleaning is 15. (i) Write down the payoff matrix of this game. Derive the dominant strategy equilibrium. Is this also a Nash equilibrium? (ii) Expiain your reasoning.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
![(a) Stan and Ollie are two students who share a flat. Both of them prefer to live in a clean flat.
However, neither is too fond of housecleaning. Each of them receives a payoff of 12 if they both
clean the flat. If neither person cleans the flat, they receive a payoff of 6 each. If one person cleans
the flat but the other person does not, then the payoff for the person who does the cleaning is 5 and
the payoff for the person who doesn't do any cleaning is 15.
(i)
Write down the payoff matrix of this game.
Derive the dominant strategy equilibrium. Is this also a Nash equilibrium?
(ii)
Expiain your reasoning.
Consider a game with N players. Each player chooses Black or White. If a player
(b)
chooses Black, she gets 100 if everyone else also chooses Black, and she gets 0 if any of the other
players does not choose Black. If a player chooses White, she always gets 50. Show that everyone
choosing Black and everyone choosing White are both Nash equilibria of this game.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7b80539c-eb0c-41a2-9ce2-3be697fd687a%2F1bb9b8b9-1088-4ec4-beaa-7684e4bf0b7c%2F1pkdtw9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) Stan and Ollie are two students who share a flat. Both of them prefer to live in a clean flat.
However, neither is too fond of housecleaning. Each of them receives a payoff of 12 if they both
clean the flat. If neither person cleans the flat, they receive a payoff of 6 each. If one person cleans
the flat but the other person does not, then the payoff for the person who does the cleaning is 5 and
the payoff for the person who doesn't do any cleaning is 15.
(i)
Write down the payoff matrix of this game.
Derive the dominant strategy equilibrium. Is this also a Nash equilibrium?
(ii)
Expiain your reasoning.
Consider a game with N players. Each player chooses Black or White. If a player
(b)
chooses Black, she gets 100 if everyone else also chooses Black, and she gets 0 if any of the other
players does not choose Black. If a player chooses White, she always gets 50. Show that everyone
choosing Black and everyone choosing White are both Nash equilibria of this game.
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