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- Design the payoffff matrix of a game with no Nash Equilibria. The game should have 2 players, 2 strategies for each player, and the payoffffs for each player should be either 0 or 1.Evaluate this statement All Nash equilibra are dominant strategy equilibria but not all dominant strategy equilibria are Nash EquilibriaProblem 3 - The Perfect Subgame Find the set of pure strategy Nash equilibria and subgame perfect equilibria of the following game: Out In 0, 20 F A F A F A -5, -5 -1,8 8,5 10, 10
- Answer all the questions, show all the working. Consider the following game in normal form. Not cooperate Cooperate Not cooperate 20,20 50,0 Cooperate 0,50 40,40 What is Nash equilibrium? Is it efficient? Why? What needs to be complied with so that the players would like to cooperate? What happens when one of the players does not cooperate? Why? Define trigger strategy. Calculate the discount factor (δ) that would make both players decide to cooperate.Iterative Elimination of Dominated Strategies Exercise 4.2 Consider the following normal form of a game. Use IEDS to reduce this game and find any Nash Equilibrium. X Y Z (60,50) (50,110) (70,90) (100,60) (70,70) (110,100) (110,70) (100,110) (40,40)parameter x =5 List all pure strategy Nash equilibria.
- Problems associated towards unique outcomes in games where multiple Nash equilibria exist”Player 2 1 2 3 1 (0,2) (1,0) (0,2) (0,2) Player 1 2 (1,0) (1,0) 3 (0,2) (1,0) (0,2) 1. Find all pure. strategy Nash equilibria 2. Does the game have a mixed strategy equilibrium? If so, find one. Otherwise, provide an explanationConsider the following normal-form game (a) Calculate the rationalizable set ? (b) Find all Nash equilibria. (c) Find all mixed-strategy Nash equilibria.
- Consider the following statements about the concept of subgame perfect Nash equilibrium (SPNE): (I) This concept only applies to finite games, not infinitely repeated games. (II) Some dynamic games might have a SPNE that is not a Nash Equilibrium. (III) The concept of SPNE rules out situations where a player would be acting against their own interest in some subgames. Group of answer choices a. Only I is correct. b. All options are incorrect. c. Only II is correct d. Only III is correct e. More than one option is correctProblem 3 Find the mixed-strategy Nash equilibria of the following game: Player 2 R 1, 4 4, 3 Player 1 C 2, 0 1, 2 1, 5 0, 6a. (D,R,A) and (U,L,B) are the only Nash equilibria in pure strategies. b. (M,R,A) and(D,R,B) are the only Nash equilibria in pure strategies. c. (D,R,A) and (D,R,B) are the only Nash equilibria in pure strategies. d. (M,R,A) and (U,L,B) are the only Nash equilibria in pure strategies. e. (D,R,A) and (M,R,B) are the only Nash equilibria in pure strategies.