讲解 Economics 201 Microeconomics Tutorial 9调试数据库编程

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?

(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?

(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?

(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?

(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:

(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?