Question 10 Consider the following payoff matrix. A U 1,1 M 2,4 D 3,3 B 3,4 2,5 0,4 M C 2,1 8,1 0,9 Indicate all the strategies that remain after you iteratively eliminate strictly dominated strategies (until no more strategies can be eliminated)
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- MIXED STRATEGY NASH EQUILIBRIUM Consider the following game in strategic form. b1 b2 a1 19,1 80,70 a2 40,50 1,19 1-п 1-0 This game has a mixed strategy Nash equilibrium (7*, o*) in which each player uses both pure strategies with strictly positive probability. Find the value of o*-n*. (Please report your answer in decimal form, rounded if necessary to the nearest 0.01.) Answer:Q-2. In order to fight for market share, two companies A and B each have the following strategies, company A has 4 strategies, namely Newspapers, Radio, TV and Social Media, while B has 3 strategies, namely Newspapers, Radio and TV. (percentage of market share.%) are as follows: Matriks Payoff: Asked: i A Koran Radio TV Sosmed B Koran Radio TV -2 1 2 3 -1 -2 -1 1 3 1 2 4 a. Does the game have a Saddle point? b. If not, determine Optimal strategy A and BMIXED STRATEGY NASH EQUILIBRIUM Consider the following game in strategic form. b1 b2 a1 18,2 80,60 a2 40,60 2,18 1-п 1-0 This game has a mixed strategy Nash equilibrium (T*,o*) in which each player uses both pure strategies with strictly positive probability. Find the value of o*-n*. (Please report your answer in decimal form, rounded if necessary to the nearest 0.01.)
- The dominant strategy of player 2 in the accompanying game is Player 1 Multiple Choice ********* 11. 12. 13. S1 S2 nonexistent. t1 11,0 10,100 Player 2 t2 6,1 5,0 t3 4,-200 0,-100please solve it in 30 minute please Consider an infinitely repeated game where the stage game is the game of chicken: Swerve Straight Swerve 0,0 -1,1 Straight 1, –1 -10, -10 Assume that the discount factor is very close to one. For concreteness, you can assume that d = 0.99. (a) Is there an SPE in which player l's payoff is 1/(1 – 6)? Explain. (b) Is there an SPE in which each player gets a payoff of 0? Explain. (c) Is there an SPE in which player l's payoff is -2/(1 – 8)? Explain.Suppose 2 players play the following game infinite times in the future. What should be the minimum value of the time discount so that the equilibrium strategy is (Cooperate, Cooperate)? Player 2 Player 1 Cooperate Defect Cooperate (10, 10) Defect (2, 12) (4,4) (12, 2)
- (ii) A mixed strategy profile (p, q) is one in which p = (p,P2.... P) is the mixed strategy of player 1, and q- (g1, q2,..q4) is the mixed strategy of player 2. Show that if p, >0 in a Nash equilibrium profile (p*, q*), the player 2 must also play i with strictly positive probability q'; > 0. (State clearly any theorem you use to show this. You are not required to justify the theorem.) %3D(b) Consider the simultaneous-move game below with two players, 1 and 2. Each player has two pure strategies. If a player plays both strategies with strictly positive probability, we call it a strictly mixed strategy for that player. Show that there is no Nash equilibrium in which both 1 and 2 play a strictly mixed strategy. Player 2 b₁ b₂ Player 1 a₁ 3,0 0,1 a2 2,1 2,1In Homework 1, we saw that there is no strict dominant strategy equilibrium in an inspection game. Thus, the players must randomize and play a mixed strategy in equilibrium. Suppose the agent shirks with probability p₁ and works with probability (1 - p₁), while the principal inspects with probability p2 and does not inspect with probability (1-P2). Find the mixed strategy equilibrium for this game. I NI S (0, -k) (w, -w) W (w c, p-w-k)| (wc, p-w) Table 1: Payoff matrix for the inspection game
- If we solve this game by elimination of dominated strategies, what payoff does Gino receive? (Gino's payoffs are located on the right of each cell, after the comma.) Gino Left Right Up (18.5, 7.4) (11.1, 33.3) Maria Down (25.9, 29.6) (14.8, 11.1) Answer:P1| P2 Left Middle Right Left 4,2 3,3 1,2 Middle 3,3 5,5 2,6 Right 2,1 6,2 3,3 Consider the simultaneous move game represented by this payoff matrix. Suppose that the game is repeated for two periods and the players know that the game will end at the end of two periods. They observe the first period outcome before they move to the second period. Assume that there is no discounting, i.e. 2nd period payoffs are not discounted, or the discount factor is equal to 1. Which of the following outcomes could occur in some subgame perfect equilibrium (SPE) of this repeated game? Choose True if you think the outcome can be a SPE, otherwise choose False. a) (Left, Left) is played in both periods. b) (Right, Right) is played in both periods. c) (Middle, Middle) is played in both periods. d) (Middle, Middle) is played in the first period, followed by (Left, Left). e) (Middle, Middle) is played in the first period, followed by (Right, Right).Under what condition can we infer that D is a dominant strategy for Player 1? Player 1 xxy.z0. x>0, y0. U D L x, 0 1, z Player 2 R 0, y z, 1