1 Player I Player 2 D EF A 10 50 20 40 30 30 30 30 20 40 10 50 B40 20 C50104020 Is there a Dominant strategy for each Player? 2. Is there a secure strategy for each player? 3. what is the Nash Equilibrium of this Game?
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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. For the following game Player B Player A Left 7,17 10,5 4,4 Middle Right 14,11 4,3 10,25 21,21 Тop Middle 14,4 Bottom 7,3 a) Determine the Nash equilibrium is any? b) Represent the game sequentially starting with player 1 and determine the sub-game perfect equilibrium c) Represent the game sequentially starting with player 2 and determine the sub-game perfect equilibrium d) Find the mixed strategy Nash equilibrium of the following game e) Firm 1 Firm 2 High price Low price High price 4,3 2,4 Low price 2,4 3,31. 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.
- 1. With nash equilibrium, do you always choose the optimal strategy? 2. Can a game have more than one nash equilibrium?Question 9 Player 1 Y Player 2 3,2 2 -0,1 1,3 -0,1 Which of the following is the Subgame Perfect Nash Equilbrium in this game?Solve for the Nash equilibrium (or equilibria) in each of the following games. (a) The following two-by-two game is a little harder to solve since firm 2’spreferred strategy depends of what firm 1 does. But firm 1 has a dominantstrategy so this game has one Nash equilibrium. Firm 2 Launch Don’tFirm 1 Launch 60, -10 100, 0 Don’t 80, 30 120, 0 What is the Nash equilibrium of this simultaneous-move game? (b) What would the outcome of this game be if instead firm 1 moved first and then, after seeing what firm 1 chose, firm 2 chose it strategy? In this case firm 1 doesn’t necessarily need to choose a best response, but firm 2 must choose a best response since it moves second.
- 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.What is the Nash Equilibrium in a game?A. A situation where all players cooperate for maximum gainB. A situation where no player can improve their outcome by changing their strategy unilaterallyC. A situation where players always choose the same strategyD. A situation where players randomly select strategies1. 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
- Player 1 Up Down [Select] Left 2,4 6,5 Player 2 In the above game, player 1 would play [Select] Right 1,0 4,2 , player 2 would play resulting in a Nash Equilibrium of [Select]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).Consider this extensive form game. The top number is player 1’s payoff, themiddle number is player 2’s payoff, and the bottom number is player 3’spayoff.a. Describe the general form of a strategy for each player.b. Find the SPNE.