Consider the following game in extensive form. A a B B B d. f h i (3, 22) (9, 5) (6,3г) (2:, 19) (15, 7) (2, 20) (7, 3z)

(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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n people guess an integer between 1 and 100, and the winner is the player whose guess is closest to the mean of the guesses + 1 (ties broken randomly). Which of the following is an equilibrium: a) All announce 1. b) All announce 50. c) All announce 75. d) All announce 100

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What is the payoff for both players in the SPNE of this game?-(2,5)-(3,4)- (2,2)- (5,1)- (1,7)

In this extensive form game, if player B is a robot uses a mixed strategy where it picks L 50% of the time and R 50% of the time. If player A chooses the action that maximizes her expected payoff, the expected payoff will be 4 07 5.5 6.5 B kw (5/1) (1,9) (48) (7.10)

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