Rick thinks either Morty or Summer broke his TV. Morty and Summer each have to decide simultaneously whether to take the blame or blame the other person. If they both blame the same person (both blame Morty or both blame Summer), the person they blame gets a small punishment and utility of -2, while the blameless person gets a utility of 0. Otherwise (if they both blame the other or both blame themselves), they both get a more severe punishment and a utility of -10.a. Draw the normal (matrix) form of this game, with Morty choosing the row and Summer choosing the column. Does either Morty or Summer have a dominant strategy? Explain your answer. Note: only Morty and Summerare players in this Game. Rick designed the game and is not a player. b. Find all Nash equilibria of this game. c. Suppose instead there are three suspects: Morty, Summer, and Jerry. Otherwise, the rules are the same as before. Draw the normal (matrix) form of the game. Hint: draw three matrices, with Morty choosing the row,Summer choosing the column, and Jerry choosing between the three matrices.d. Find all Nash equilibria of the three-player game from part (c). e. Suppose the game is played sequentially, with Summer moving first, Morty second, and Jerry third. Draw the game tree and find all subgame-perfect equilibria of the sequential game. f. Does the sequential game have a Nash equilibrium that is not subgame perfect? Explain your answer.
Rick thinks either Morty or Summer broke his TV. Morty and Summer each have to decide simultaneously whether to take the blame or blame the other person. If they both blame the same person (both blame Morty or both blame Summer), the person they blame gets a small punishment and utility of -2, while the blameless person gets a utility of 0. Otherwise (if they both blame the other or both blame themselves), they both get a more severe punishment and a utility of -10.
a. Draw the normal (matrix) form of this game, with Morty choosing the row and Summer choosing the column. Does either Morty or Summer have a dominant strategy? Explain your answer. Note: only Morty and Summer
are players in this Game. Rick designed the game and is not a player.
b. Find all Nash equilibria of this game.
c. Suppose instead there are three suspects: Morty, Summer, and Jerry. Otherwise, the rules are the same as before. Draw the normal (matrix) form of the game. Hint: draw three matrices, with Morty choosing the row,
Summer choosing the column, and Jerry choosing between the three matrices.
d. Find all Nash equilibria of the three-player game from part (c).
e. Suppose the game is played sequentially, with Summer moving first, Morty second, and Jerry third. Draw the game tree and find all subgame-perfect equilibria of the sequential game.
f. Does the sequential game have a Nash equilibrium that is not subgame perfect? Explain your answer.
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