Question C2. Consider the two player game depicted in the payoff matrix below: Player 2 A B (5, 2) (0, 6) Y (1, 0) | (-1, 3) Z (2, 6) (10, 0) a) Explain what a mixed strategy is and provide an example of a real-life game in which we might observe players adopting such strategies. b) Determine all pure and mixed Nash Equilibria for this game. c) Suppose that the payoffs in the game changed such that X and A became dominant strategies for players 1 and 2 respectively, would this change the result from part (b)? Explain your answer. Player 1

Question C2. Consider the two player game depicted in the payoff matrix below: Player 2 A B (5, 2) (0, 6) Y (1, 0) | (-1, 3) Z (2, 6) (10, 0) a) Explain what a mixed strategy is and provide an example of a real-life game in which we might observe players adopting such strategies. b) Determine all pure and mixed Nash Equilibria for this game. c) Suppose that the payoffs in the game changed such that X and A became dominant strategies for players 1 and 2 respectively, would this change the result from part (b)? Explain your answer. Player 1

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.1P

See similar textbooks

Similar questions

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.
A and B are competitors in the mobile phone industry. Both A and B have to decide whether to participate or not to participate in a Phone for the Future Trade Fair next month. The matrix payoff below shows the profits (USD million) corresponding to their actions. a) What is the Nash equilibrium of the above game? b) Is the Nash equilibrium Pareto Optima? Explain. c) Suppose B is pessimistic of A's rationality, what is B's strategy? Compare and comment on B's strategy in (a) and (c). A Participate Do not participate B Participate Do not participate 400,1000 200,200 500,500 1000,400
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) None
Consider a two-player game in which the players take turns, with player 1 moving first. When it is a player's turn, she must announce a number between 1 and 3. The announced number is added to the previously announced numbers. The player who announces the number such that the sum of all announced numbers is 6 wins (receives 1) and the other loses (receives 0). Please indicate whether or not each of the following sequences of announcements is a Nash equilibrium of the game. Hint: Think about how one verifies whether or not a pair of strategies is a Nash equilibrium. P1 says 3, then P2 says 2, then P1 says 1 P1 says 1, then P2 says 3, then P1 says 2 P1 says 2, then P2 says 3, then P1 says 1 P1 says 3, then P2 says 1, then P1 says 2
Suppose B = [bj] is the m x n payoff matrix of a 2-person zero-sum simultaneous game a. Let a' be the 2-person zero-sum simultaneous game with payoff matrix B' = [b,g) = [b.j + a] for some constant a e R. Show that if (, T) is a Nash equilibrium of a and the value of a is v*, then ( , 7') is also a Nash equilibrium of a' and the value of a' is v* + a.
For a two-player game, the payoff function for player 1 is V1(x1, x2) = x1 + 10x1x2and for player 2 is V2(x1, x2) = x2 + 20x1x2.Player 1’s strategy set is the interval [0,100], and player 2’s strategy set is theinterval [0,50]. Find all Nash equilibria.
D Question 11 Consider the following Extended Form Game: O 1 02 O 3 A' 04 (9,5) A P2 P1 B' A' (5,2) (8,5) B x A (1,6) P2 B' According to backwards induction, in how many turn does the game end? P1 B (6,7)
Find the Nash Equilibria for each of the following 2x2 games (The left payoff value is associated with the strategies (1 or 2) while the right payoff value is associated with the strategies (A or B)): (a) (b) (c) (d) B 1 3,3 2 4,4 5,5 1 2 1 2 1 2 A 2,2 24 A B 2,5 0,3 4,0 -5,2 A 1,0 0,6 B 4,1 5,5 A B -1,-3 -3,2 -4,1 0,0
Consider the following game matrix with two players- Player 1 and Player 2 with their respective strategies. Which of the following statements is correct such as x>y>b>a Players Player2 Player 1 A B C D (Y, Y) (b, x) (x, a) (AE) is the one of many Nash equilibria (C) is the unique Nash equilibria (C. D) is the unique Nash equilibria (A. E) and (B. F) are two Nash equilibria E (a, b) (x, y) (y, a) F (a,x) (a, b) (b, b)
Provide an example of a 2-player normal form game where each player has 3 (pure) strategies such that: (i) There is no pure strategy Nash equilibrium.
Use the following payoff matrix for a one-shot game to answer the accompanying questions. Player 2 Strategy X Y Player 1 A 50, 50 -110, 6 B 6, -110 26, 26 a. Determine the Nash equilibrium outcomes that arise if the players make decisions independently, simultaneously, and without any communication.check all that apply (26,26) (50,50) (-110,6) (6,-110) Which of these outcomes would you consider most likely?multiple choice 1 (-110,6) (50,50) (6,-110) (26,26) b. Suppose player 1 is permitted to “communicate” by uttering one syllable before the players simultaneously and independently make their decisions. What should player 1 utter?multiple choice 2 B A What outcome do you think would occur as a result?multiple choice 3 (26,26) (50,50) (-110,6) (6,-110) c. Suppose player 2 can choose its strategy before player 1, that player 1 observes player 2’s choice before making her decision, and that this move…