Economics 201 Microeconomics
Tutorial 9
Question 1:
Consider the following two player game. The first number in each cell refers to the payoff to Player 1 while the second number refers to the payoff to Player 2. Players move simultaneously. Which of the following statements is INCORRECT?
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Player #1
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Player #2
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Left
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Right
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Top
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7, 7
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0, 4
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Bottom
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4, 0
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4, 4
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(a) This game has two Nash equilibria: {Top, Left} and {Bottom, Right}.
(b) {Top, Left} is the payoff dominant outcome.
(c) If players are excessively risk-averse then we could see a relatively high proportion of {Bottom, Right} outcome.
(d) {Bottom, Right} is the payoff dominant outcome.
Question 2:
Consider the following two player game. The first number in each cell refers to the payoff to Player 1 while the second number refers to the payoff to Player 2. Players move simultaneously. Which of the following statements is CORRECT?
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Player #1
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Player #2
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Left
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Right
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Top
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8, 14
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8, 8
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Bottom
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10, 6
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12, 8
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(a) Player #1 has a dominant strategy, Bottom; there is a unique Nash Equilibrium in this game and that is {Bottom, Right}.
(b) Player #2 has a dominant strategy, Right; there is a unique Nash Equilibrium in this game and that is {Bottom, Right}.
(c) Player #1 has a dominant strategy, Bottom; player #2 has a dominant strategy, Right; there is a unique Nash Equilibrium in this game and that is {Bottom, Right}.
(d) There are two Nash equilibria in this game – {Top, Right} and {Bottom, Left}.
Question 3:
Consider the following two player game. The first number in each cell refers to the payoff to Player 1 while the second number refers to the payoff to Player 2. Players move simultaneously. Which of the following statements is INCORRECT?
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Player #1
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Player #2
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Left
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Right
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Top
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5, 3
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0, 0
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Bottom
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0, 0
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3, 5
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(a) There are two equilibria in this game: {Top, Left} and {Bottom, Right}.
(b) In the mixed strategy equilibrium of this game, Player 1 should play Top with probability 5/8 and Bottom with probability 3/8; Player 2 should play Left with probability 3/8 and Right with probability 5/8.
(c) In the mixed strategy equilibrium of this game, Player 1 should play Top with probability 3/5 and Bottom with probability 2/5; Player 2 should play Left with probability 2/5 and Right with probability 3/5.
(d) Players would prefer to coordinate to one of the equilibria, either {Top, Left} or {Bottom, Right} rather than end up at either {Top, Right} or {Bottom, Left}.
Question 4:
Consider the following two player game. In each cell the first number refers to the payoff to Player 1 while the second number refers to the payoff to Player 2. Suppose the two players move simultaneously (at the same time). Which one of the following statements is correct?
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Player #1
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Player #2
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Left
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Right
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Top
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7, 7
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0, 4
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Bottom
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4, 0
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4, 4
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(a) In the mixed strategy equilibrium of this game, Player 1 should play Top with probability 4/7 and Bottom with probability 3/7; Player 2 should play Left with probability 4/7 and Right with probability 3/7.
(b) There is a unique dominant strategy Nash equilibrium at {Bottom, Right}
(c) In the mixed strategy equilibrium of this game, Player 1 should play Top with probability 2/5 and Bottom with probability 3/5; Player 2 should play Left with probability 2/5 and Right with probability 3/5.
(d) In the mixed strategy equilibrium of this game, both players should randomize over the strategies with probability ½ and ½.
Question 5:
Consider the following two-player game with players moving sequentially. Player 1 moves first and can choose to either “Take” or “Pass”. If Player 1 chooses “Take” then the game ends immediately and Player 1 gets $8 and Player 2 gets $12. If Player 1 chooses “Pass” then Player 2 gets to move. Player 2 can choose “Take” or “Pass”. If Player 2 chooses “Take” then the game ends immediately. Player 1 gets $10 and Player 2 gets $15. If Player 2 chooses “Pass” then Player 1 gets to move again. Player 1 can choose “Take” or “Pass”. In either case the game ends after Player 1’s move. If Player 1 chooses “Take” then Player 1 gets $20 and Player 2 gets $10. If Player 1 chooses “Pass” then Player 1 gets $10 and Player 2 gets $20. Which of the following statements is CORRECT?
(a) Player 1 should choose to “Take” at the very first opportunity to move.
(b) Player 2 should choose to “Take” at the very first (and really only) opportunity to move.
(c) Player 1 should choose to “Pass” in his/her second opportunity to move.
(d) Player 2 should choose to “Pass” at the very first (and really only) opportunity to move.
Question 6:
Consider the following two player game. In each cell the first number refers to the payoff to Player 1 while the second number refers to the payoff to Player 2. If Player 1 moves first and player 2 follows, then using the principle of backward induction the subgame perfect equilibrium of this game is:
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Player #1
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Player #2
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Left
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Right
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Top
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8, 4
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2, 2
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Bottom
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2, 2
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4, 8
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(a) Top, Left.
(b) Top, Right.
(c) Bottom, Left.
(d) Bottom, Right.
How would the outcome of the game change if Player #2 moved first?