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Q) reduce the payoff matrix by dominance. Find optimal Statragy for each player and the value of game.
Given meaning full answer plz .payoff matrix given in image
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- 6. Consider the following two-player game: 2 L M U 3,3 2,3 1 M 2,1 3,1 D R 0,2 3,3 0,3 3,0-5, -5 a. Find all pure NE. b. Find a (non-pure) MNE in which player 1 (the row player) plays a pure strategy. c. (Harder Question) Show that there cannot be a CE prescribing that strat- egy D of player 1 (the column player) is played with positive probability.Consider the following two-player game with three options for each player. (Payouts are listed for the row player first, then the column player.) player Y layery 3,3 A 1,5 4,4 6,2 K 8,1 3,7 5,2 0,6 1,1 Find a mixed Nash equilibrium for this game. Solution suggestion: Use two variables per player. If p and are the probabilities of selecting the first two strategies, then 1-p-q is the probability of selecting the third strategy. You will need to solve a system of equations.Player 1 Cooperate (C) Defect (D) If the game has a dominant strategy, what is it? There is none. If the game has a Nash equilibrium in pure strategies, what is it? There is none. Cooperate (C) 3,3 8,0 Cooperate (C) is a dominant strategy for both players. Defect (D) is a dominant strategy for both players. Cooperate (C) is a dominant strategy for 1, and Defect (D) is a dominant strategy for 2. C, C is the only Nash equilibrium. D, D is the only Nash equilibrium. C, C and D, D are both Nash equilibria. Player 2 Defect (D) 0,8 1,1
- Find all NE of the stage game.(b) Consider a two-period game without discounting in which the stage game is played ineach period. Find all pure strategy SPNE.(c) What’s the min-max payoff of each player?(c1) Consider pure strategies only.(c2) Consider all strategies, including the mixed ones.(d) Now suppose the stage game is repeated infinitely many times. Use the Fudenberg-Maskin Folk theorem to find all possible values of payoff that can be supported as aSPNE.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.Player 1 Cooperate (C) Defect (D) Cooperate (C) 3,3 8,0 Player 2 Defect (D) 0,8 1,1 In general, a combination of strategies is a Nash equilibrium if ... Every player is choosing a best response against the other players' strategies. Every player has a positive payoff. The players maximize the sum of their payoffs. The players choose identical strategies. If the game is repeated, which cooperative actions could benefit both players? O Both players choose C. Player 1 chooses C, Player 2 chooses D. O Player 1 chooses D, Player 2 chooses C. Both players choose D.
- 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 BPlayer 2 A B C А 2, 2 6,1 1,1 Player 1 B 1,6 5,5 1,1 1,1 1,1 4,4 Consider the simultaneous move game represented in normal form by this payoff matrix. Suppose that the game is repeated for two periods. 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. (B, B) is played in the first period, (C, C) is played in the second period. (A, A) is played in both periods. (C, C) is played in both periods.Consider the following infinitely repeated game: 1/2 C D с 2,2 -3,3 D 3,-3-2,-2 a. Start with C and continue playing C as long as neither player deviates. If any player deviates, play D from that point onwards. For what value of the discount factor will this strategy be subgame perfect. b. Start with C, D and alternate between C,D and D,C. In case of deviation, play D,D forever. Can this strategy be subgame perfect?
- 1. Consider the following normal form game. X Y (a) What is the set of rationalizable strategies for this game? Player 1 Player 2 W Q 1,7 1,5 2,3 Z 3,4 0,4 0,6 R= (b) The game has only one Nash equilibrium and it is a mixed strategy Nash equilibrium. Compute and report this equilibrium. Equil. strategy profile:1. Static and Dynamic Game. Consider the following 2-by-2 game: C D 1A (1,10) (1,1) B (2, a) (0,1) (a) erwise, find the pure-strategy Nash equilibria, if any of this game. (There is no need to look for equilibria in mixed strategies) Assume for now that a = 2. Using dominant strategies or oth- (b) Now, consider the dynamic game in which player 1 moves before player 2, and the payoffs remain unchanged. i.: possible strategies for each player? Recall that a strategy profile for a player not at the initial node of the game tree must specify an action for the player at every node. Draw the game tree for this dynamic game. What are the ii "Find the backward-induction solution(s) to this game. Calculate the equilibrium payoffs for each player. Com- pared to the simultaneous game, is there a first-mover advantage or a ii. second-mover advantage? (c) Now, assume that a = 0 in the original static game. i. Find all the Nash equilibria in pure and mixed strategies. Denoting p the probability…In game theory, each player is assumed to have the following, except Multiple Choice O O O O alternative strategies or actions. alternative outcomes or results. alternative payoffs or earnings. alternative partners or coplayers.
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