ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN: 9780190931919
Author: NEWNAN
Publisher: Oxford University Press
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Question
Use the following normal-form game to answer the questions below.
| Player 2 | |||
| Strategy | C | D | |
| Player 1 | A | 50, 50 | 120, 25 |
| B | 25, 120 | 55, 55 |
a. Identify the one-shot Nash equilibrium.
multiple choice 1
-
(B,C)
-
(B,D)
-
(A,C)
-
(A,D)
b. Suppose the players know this game will be repeated exactly three times. Can they achieve payoffs that are better than the one-shot Nash equilibrium?
multiple choice 2
-
No
-
Yes
c. Suppose this game is infinitely repeated and the interest rate is 6 percent. Can the players achieve payoffs that are better than the one-shot Nash equilibrium?
multiple choice 3
-
No
-
Yes
d. Suppose the players do not know exactly how many times this game will be repeated, but they do know that the probability the game will end after a given play is θ. If θ is sufficiently low, can players earn more than they could in the one-shot Nash equilibrium?
multiple choice 4
-
Yes
-
No
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- 1. Consider the following N-player game. Each agent has a choice of strategy A or B. The state variable is x, the proportion of agents choosing strategy A. For every agent, the utility of choosing strategy A is U(A) = 10 +2x and the utility of choosing strategy B is U(B) = 10+3x. What is the Nash equilibrium to this game? Explain.arrow_forwardQUESTION 2 In the game above, what is/are the sub-game perfect Nash equilibrium? (up, up) (up, down) ( down, up) (down, down) No equilibrium exists QUESTION 2 Up Down Player 1 No equilibrium exists Up In the game above, what is/are the sub-game perfect Nash equilibrium? (up,up) (up,down) (down, up) □ (down, down) Down Up Down Player 2 P1 gets $45 P2 gets $155 P1 gets $100 P2 gets $10 P1 gets $85 P2 gets $85 P1 gets $95 P2 gets $95arrow_forwardQUESTION 3 Up Down In the game above, what is/are the sub-game perfect Nash equilibrium? Ⓒ (up,up) (up,down) Player 1 (down, up) (down, down) No equilibrium exists Up Down Up Down Player 2 P1 gets $25 P2 gets $25 P1 gets $7 P2 gets $30 P1 gets $13 P2 gets $9 P1 gets $8 P2 gets $6arrow_forward
- Problem 2. Consider the partnership-game we discussed in Lecture 3 (pages 81-87 of the textbook). Now change the setup of the game so that player 1 chooses x = [0, 4], and after observing the choice of x, player 2 chooses y ≤ [0, 4]. The payoffs are the same as before. (a) Find all SPNE (subgame perfect Nash equilibria) in pure strategies. (b) Can you find a Nash equilibrium, with player 1 choosing x = 1, that is not subgame perfect? Explain.arrow_forwardPlayer 2 Left Right P1: $4 Player 1 Up P2: $1 P1: $10 Down P2:s10 Which of the Nash Equilibrium to this game are efficient? [Check all that apply] A) (up, left) B) (down, left) C None are efficient (D) (up right) E (down, right) Last saved 4:31:15 PM P1:S1 P2: $6 P1: $0 P2: $11 Gradingarrow_forwardUp Down Up Up Down Down Player 1 Player 2 In the game above, what is/are the EFFICIENT sub-game perfect Nash equilibrium? (up,up) (up,down) (down, up) (down, down) No EFFICIENT equilibrium exists P1 gets $45 P2 gets $155 P1 gets $100 P2 gets $10 P1 gets $85 P2 gets $85 P1 gets $95 P2 gets $95arrow_forward
- Consider a simultaneous game where player A has a dominant strategy and player B has two strategies (none of which is a dominant strategy). How many pure strategy Nash equilibria will this game have? A) Exactly 1 B) Exactly 2 C) Either 1 or 2 D) Nonearrow_forward1.9. What is a mixed strategy in a normal-form game? What is a mixed-strategy Nash equilibrium in a normal-form game?arrow_forwardIn a small town there are two pizza restaurants . If neither restaurant advertises, its revenue will not change. If only one firm advertises, the firm that advertises will double its revenue and the firm that doesn't advertise will see a decrease in its revenue, but if both firms advertise, their revenue will not change. What outcome would be predicted by game theory in this market? Both restaurants will advertise. Game theory would predict chat sometimes one restaurant would advertise, and the rest of the time both will advertise. Neither restaurant will advertise Game theory is only a theory and cannot predict real-world events. One restaurant will advertise.arrow_forward
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