H L H 12, 8 2, 3 L 3,2 4, 4 The numbers in each cell of the matrix above, (m₁, m2), represents monetary payments that two players receive based on their choices of actions {H, L}. Refer to this table for questions 1-2 below. 1. Assume that the utility of each player equals to the amount of money she gets (that is, the matrix above represent the payoffs in the game). Denote by p the probability that player 1 picks the action H (that is, p summarized Player 1's strategies given that there are only two actions). Similarly, denote by q the probability that player 2 chooses to play H. Which of the following statements is true about the mixed strategy Nash equilibrium (NE) for this game? (a) p has to be such that player 2 is indifferent between choosing H and L (b) p has to be such that player 1 is indifferent between choosing H and L (c) Player 1 can never be indifferent between playing H and L in any NE (d) The game has no mixed strategy Nash equilibrium. (e) p and q are both equal to ½ in the mixed strategy NE 2. Which of the following characterizes the Nash Equilibrium where at least one player uses a strictly mixed strategy? (a) The game has no mixed strategy Nash equilibrium. (b) p= == (c) p = 1,9= }}} (d) p= (e) p= = 1,9 = 11 3. Titanium Dioxide, the base chemical used to make white paint, is produced by two base chemical companies. These companies compete a la Cournot. The market inverse demand function is given by P(Q) = 8-Q. Assume that both firms have the total cost functions C(q) 1+2q. Let the star superscript* denote equilibrium quantities/prices/profits. Which of the following statements is true? (a) q* = q = 4 (b) π₁ =π=3 (c) p* = 6 (d) л<л½ (e) π₁ = π₁₂ = 4
H L H 12, 8 2, 3 L 3,2 4, 4 The numbers in each cell of the matrix above, (m₁, m2), represents monetary payments that two players receive based on their choices of actions {H, L}. Refer to this table for questions 1-2 below. 1. Assume that the utility of each player equals to the amount of money she gets (that is, the matrix above represent the payoffs in the game). Denote by p the probability that player 1 picks the action H (that is, p summarized Player 1's strategies given that there are only two actions). Similarly, denote by q the probability that player 2 chooses to play H. Which of the following statements is true about the mixed strategy Nash equilibrium (NE) for this game? (a) p has to be such that player 2 is indifferent between choosing H and L (b) p has to be such that player 1 is indifferent between choosing H and L (c) Player 1 can never be indifferent between playing H and L in any NE (d) The game has no mixed strategy Nash equilibrium. (e) p and q are both equal to ½ in the mixed strategy NE 2. Which of the following characterizes the Nash Equilibrium where at least one player uses a strictly mixed strategy? (a) The game has no mixed strategy Nash equilibrium. (b) p= == (c) p = 1,9= }}} (d) p= (e) p= = 1,9 = 11 3. Titanium Dioxide, the base chemical used to make white paint, is produced by two base chemical companies. These companies compete a la Cournot. The market inverse demand function is given by P(Q) = 8-Q. Assume that both firms have the total cost functions C(q) 1+2q. Let the star superscript* denote equilibrium quantities/prices/profits. Which of the following statements is true? (a) q* = q = 4 (b) π₁ =π=3 (c) p* = 6 (d) л<л½ (e) π₁ = π₁₂ = 4
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.11P
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Transcribed Image Text:H
L
H
12, 8
2, 3
L
3, 2
4,4
The numbers in each cell of the matrix above, (m₁, m2), represents monetary payments that two
players receive based on their choices of actions {H, L}. Refer to this table for questions 1-2 below.
1. Assume that the utility of each player equals to the amount of money she gets (that is, the
matrix above represent the payoffs in the game). Denote by p the probability that player 1
picks the action H (that is, p summarized Player 1's strategies given that there are only two
actions). Similarly, denote by q the probability that player 2 chooses to play H. Which of the
following statements is true about the mixed strategy Nash equilibrium (NE) for this game?
(a) p has to be such that player 2 is indifferent between choosing H and L
(b) p has to be such that player 1 is indifferent between choosing H and L
(c) Player 1 can never be indifferent between playing H and L in any NE
(d) The game has no mixed strategy Nash equilibrium.
(e) p and q are both equal to ½ in the mixed strategy NE
2. Which of the following characterizes the Nash Equilibrium where at least one player uses a
strictly mixed strategy?
(a) The game has no mixed strategy Nash equilibrium.
(b) p=
(c) p = 3,9 =
(d) p = 3,9=
= 2,9 = 1
(e) p=
3. Titanium Dioxide, the base chemical used to make white paint, is produced by two base
chemical companies. These companies compete a la Cournot. The market inverse demand
function is given by P(Q) = 8- Q. Assume that both firms have the total cost functions
C(q)=1+2q. Let the star superscript* denote equilibrium quantities/prices/profits. Which
of the following statements is true?
(a) q* = q = 4
(b) π₁ =π=3
(c) p* = 6
(d) л <π½
(ε) π = _ = 4
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