(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.

Managerial Economics: A Problem Solving Approach
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Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
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Chapter18: Auctions
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(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.
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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