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 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 =, q=2 (c) p =, q= (d) p = , q= }} 2 2 a= (e) n =

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 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 =, q=2 (c) p =, q= (d) p = , q= }} 2 2 a= (e) n =

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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H
L
at 11:59 pm Pacific time
H L
12,8
2,3
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?
(d)
= 3,9 = /
(e) p = ²1, q = 11
(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 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 =
= 33,9 = ²/₁
(c) p = 3,q =

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