1. Use the following one-shot, normal form game to answer the questions below. Strategy A 100, 125 300, 250 200, 100 500, 500 400, 300 -100, 350 250, O 750, 400 0, -100 (a) Find each player's dominant strategy, if it exists. (b) Find the Nash equilibrium.
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- Aedri Quick Lesson in Game Theory A Nash Equilibrium is an outcome in which neither player is better off by changing their strategy. 2.7 Is a Dominant Strategy equilibrium also a Nash equilibrium? a) Yes b) No esc The Ice Cream Guys $3.99 $4.99 + Chucky's Chunky CCT: $20,000 $3.99 ICG: $20,000 CCT: $60,000 ICG: $10,000 tab Treats CCT: $10,000 $4.99 ICG: $60,000 CCT: $40,000 ICG: $40,000 The table above is the payoff matrix for the annual profit of the only two ice-cream-truck firms operating in Beach City. They are deciding the price of an ice cream cone. %3D caps lo 2.8 What is Chucky's dominant strategy? a) $3.99 b) $4.99 c) Not enough information hift 2.9 What is the dominant strategy equilibrium in this situation? a) Both charge $3.99 b) Both charge $4.99 c) CCT charges $3.99 and ICG charges $4.99 d) CCT charges $4.99 and ICG charges $3.99 2.10 Suppose these two firms engaged in collusion (which, of course, totally doesn't happen because it is against the law). Which outcome would…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).1. With nash equilibrium, do you always choose the optimal strategy? 2. Can a game have more than one nash equilibrium?
- Problem 1. You are given the following bimatrix games. For each one, find all pure Nash equilibria. (a) (Prisoner's Dilemma) Player 2 Quiet 2, 2 3,0 Fink Quiet Fink 0,3 1,1 Player 1 (b) (Matching Pennies) Player 2 Нead Head 1,-1 Tails -1,1 Player 1 Tails -1,1 | 1, -1 (c) (Battle of the Sexes) Girl OK, football... OK, theatre... Football! Theatre! 1,5 0,0 0,0 5,1 Boy (d) (Battle of the Sexes... modified) Girl Football great, I will invite my dad Theatre! OK, football... OK, theatre... Football! 1,5 0,0 0,0 5, 1 0,0 -1 , 2 Boy4.Use the following normal-form game to answer the questions below. Strategy D A 10, 10 60, -5 -5, 60 50, 50 (a) Identify the one-shot Nash equilibrium. (b) Suppose the game is infinitely repeated and the interest rate is 5%. Can the players achieve payoffs that are better than the one-shot Nash equilibrium? Explain.5. Aaron and Betty play the following one-shot game. Aaron Up Middle Down Left 10,0 5,10 1,1 Betty Right 0,5 1,0 2,2 a. Does the game above have any (pure strategy) Nash equilibria? Find any equilibria or explain why an equilibrium doesn't exist. b. Suppose instead that Aaron moves first and Betty moves second. Represent this situation with a game tree and find the subgame perfect Nash equilibrium. Are Aaron and Betty better off playing a simultaneous game or a sequential game in which Aaron moves first? Explain. c.
- 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.Quick Lesson in Game Theory A Nash Equilibrium is an outcome in which neither player is better off by changing their strategy. 2.7 Is a Dominant Strategy equilibrium also a Nash equilibrium? a) Yes b) No The Ice Cream Guys $3.99 $4.99 Chucky's Chunky CCT: $20,000 $3.99 ICG: $20,000 CCT: $60,000 ICG: $10,000 CCT: $10,000 $4.99 ICG: $60,000 CCT: $40,000 ICG: $40,000 Treats The table above is the payoff matrix for the annual profit of the only two ice-cream-truck firms operating in Beach City. They are deciding the price of an ice cream cone. 2.8 What is Chucky's dominant strategy? a) $3.99 b) $4.99 c) Not enough information 2.9 What is the dominant strategy equilibrium in this situation? a) Both charge $3.99 b) Both charge $4.99 c) CCT charges $3.99 and ICG charges $4.99 d) CCT charges $4.99 and ICG charges $3.99 2.10 Suppose these two firms engaged in collusion (which, of course, totally doesn't happen because it is against the law). Which outcome would they agree upon, if any? a) Both…Which is the correct mixed strategy Nash equilibrium for the below game? A B Confess Confess (3,2) Doesn't (0,0) confess a. (2/5); (3/5) b. (1/4); (3/4) c. (1/2); (1/2) d. (1/3); (2/3) Doesn't confess (0,0) (2,3)
- 2. Brad and Angelina have agreed to meet up for their first date. Neither of them can remember the exact location where they arranged to meet up and have forgotten their phones at home. Their payoff matrix can be described as follows: Brad The Hive Le Monde a) What is the Nash equilibrium in this game? Angelina The Hive 5; 5 0; 0 Le Monde 0; 0 5; 5Suppose that Green Giant and Red Rover are two companies competing in the canned vegetable market. Each is contemplating an aggressive new ad campaign. The payoffs of each decision are listed below, where Green Giant is player 1. Green/Red Ad Campaign No Ad Campaign |Ad Campaign |1 million, 1 million zero, 3 million No Ad Campaign 3 million, zero 2 million, 2 million What is the Nash equilibrium of the game? a. (advertise, don't advertise) b. (advertise, advertise) c. (don't advertise, don't advertise) d. (don't advertise, advertise)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.