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- 16. A subgame perfect Nash equilibrium is: (a) A process for solving dynamic games by starting at the end and working backwards. (b) A solution concept used in dynamic games of complete information. (c) A method for finding the optimal strategy in a dynamic game. (d) An outcome of a dynamic game which is Pareto optimal. (e) All of the above.3. (a) Give an example of a 3 x 3 zero-sum game where all possible pairs of pure strategies give a pure Nash Equilibrium. (b) Describe all possible 3 x 3 non-zero-sum games where all possible pairs of pure strategies give a pure Nash Equilibrium. Give reasons for your answer.Address the following with suitable examples. (a)How Nash Equilibrium is achieved under Game Theory. (b)Find Nash Equilibrium in case of first-mover strategy. (c)Give some examples of games with two Nash Equilibriums? (d)Explain the concept of Nash Equilibrium in case of Non-Cooperative Games. (e)How expected Nash Equilibrium would be achieved in case of game with no Nash Equilibrium?
- a) How many players does this game have? What are the strategies of each player? (b) What are the Nash equilibria of this game? (c) What are the Pareto Efficient outcomes?(a) Compute the Nash Equilibrium in pure strategies of the game above. (b) Compute the subgame perfect Nash equilibrium.(c) Compute the perfect Bayesian euilibrium. (I need help with how to solve these questions in detail)3. For each of the following statements, say whether it is true or false, and explain your answer. (a) "A roll-back equilibrium is not a Nash equilibrium." (b) "If a simultaneous-move game has pure strategy equilibria, the game cannot have mixed strategy equilibria too. (c) "Players who have a strictly dominant pure strategy will never choose to play a mixed strategy."
- 1. Use the following one-shot, normal form game to answer the questions below. Strategy A 100, 125 300, 250 200, 100 250, 0 500, 500 750, 400 400, 300 -100, 350 0, -100 (a) Find each player's dominant strategy, if it exists. (b) Find the Nash equilibrium.24. Two individuals play the following infinitely repeated prisoner's dilemma game: Player A Cooperate Defect Player B Cooperate 3,5 7,0 Defect 0,6 1, 1 Assume that both players discount future payoffs at rate 8<1. (a) If both players play 'cooperate' every period, then what are their total payoffs?1. You (row)/Your Crush (column) McElroy Corcoran The Dining Hall Game McElroy 3,2 0,0 a) Represent this game in extensive form b) How many subgames does this game have? Corcoran 1,1 2,3
- 1. Consider the following normal-form game: Player 2 Left Right 30,20 10,10 10,30 20,20 Player 1 How many pure-strategy Nash Equilibria are there in this game? (a) 0 (b) 1 Up Down (c) 2 (d) 3 (e) 4 (f) None of the above Answer: 1b. The only Nash Equilirbium is (Up,Left).26. Consider the following game. There are ten churches in town: nine are Catholic and one is Eastern Orthodox. All churches conduct their services at 10am on Sunday morning. You and your friend, without communication, agree to meet at a church service. If you fail to meet at the same church, then you are sad. What is this game's focal point? Remember that you cannot communicate about this. (A) You meet at any of the Catholic churches. (B) You meet at any of the churches – denomination does not matter. (C) You meet at the Orthodox church. (D) There is no focal point. 27. Which of the following is the best example of Skin in the Game? (A) A politician retires to serve on the board of governors of a prestigious think tank. (B) A wealthy man donates his savings to charity. (C) A general leads his troops into battle. (D) Billie Eilish creates another cringe music video. 28. Public choice theory makes assumptions about the motives of politicians, firms, voters, and bureaucrats. Which of…8) Consider the following game: There are 10 players. Each player is asked to write a number between 0 and 100. The player whose choice is closest to half of the average is the winner. Describe the game and discuss what would you expect to be the average number if the game were played in class with your colleagues. Do you expect them to play the Nash equilibrium strategy? Explain.
