3.a. What are Firm I's possible strategies? And what are Firm E's possible strategies? 3.b. With the help of strategies, write down the normal form representation of the game. 3.c. Write down the representation of the two firms' mixed strategy.
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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…5. For the strategic form game shown, derive the strategies that survive the IDSDS. Player 2 y 5,2 3,4 2,1 4,4 3,2 3,3 Player 1 3,5 4,4 0,4 2,3 1,5 3,0b 500,0 -10, 30 B 6,-1 0,0 C -1, 20 -20, 100 What is the Nash Equilibrium of this game? A a a. (C, c) O b. (C, b) O c. (A, a) O d. (B, b) C 20, 12 8, -2 7,800
- し(5,3) b I(2,2) も(0,0) (4,12) a (12.4) (0,0) i). List all subgame pertect Nash equilibria and name one Nash eqvilibrivm that is not subgame pertect i). How many strategies does playot and player 2 have?rock paper scissors гock 0. -3 1 рарer 1. -1 scissors -1 3 0. (a) Show that xT= ( ) and yT= (3) together are not a Nash equilibrium 3 3 313 for this modified game. (b) Formulate a linear program that can be used to calculate a mixed strategy x € A(R) that maximises Rosemary's security level for this modified game. (c) Solve your linear program using the 2-phase simplex algorithm. You should use the format given in lectures. Give a mixed strategy x E A(R) that has an optimal security level for Rosemary and a mixed strategy y E A(C) that has an optimal security level for Colin.he following payoff matrix represents a non-sequential, non-repeating game: Brown Inc. Strategy 1 Strategy 2 Strategy 3 100 300 400 Strategy A 40 70 30 Carlton Inc. 700 200 600 Strategy B 60 20 80 500 90 a) Name the maximin equilibrium, if any. (If there is no maximin equilibrium, then please type 'there is no maximin equilibrium.) b) Name the maximax equilibrium., if any. (If there is no maximax equilibrium, then please type 'there is no maximax equilibrium.) C) Name the Nash equilibrium, If any. (If there is no Nash equilibrium, then please type 'there is no Nash equilibrium.) 220 800 Strategy C 10 50 d) Name the cooperative (collusive) equilibrium, if any. (If there is no cooperative equilibrium, then please type 'there is no cooperative equilibrium.) e) Name Brown Inc's dominant strategy, if any. (If Brown Inc. has no dominant strategy, then please type 'Brown Inc. has no dominant strategy.) f) Name Carlton Inc's dominant strategy, if any. (If Carlton Inc. has no dominant strategy,…
- 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 3,33. Determine the Nash Equilibrium for the following normal form of the game. A) MARY B) UP DOWN PLAYER 1 HARLEY UP (10, 10) (4,8) LEFT (3,0) UP MIDDLE (1, 1) DOWN (0,1) DOWN (8,4) (5,5) PLAYER 2 CENTER RIGHT (2,1) (1,1) (4,2) (0,0) (5,0) (0,1)28 A payoff matrix shows the payoffs (i.e. bribes) required to government officials for firms undertaking specific actions. A details the actions each firm takes. shows the payoffs to each firm for each possible outcome. is optional in game theory. 29 A player's best response is the strategy that maximizes his payoff given what he thinks the other player will do. a dominant strategy. A В impossible to find when there isn't a Nash equilibrium. a way to avoid the prisoners' dilemma. D 30 Strategic advertising in the cola market significantly expands the size of the market. brings in few new customers and primarily shifts market share among A В rivals. shifts market demand to the right, increasing quantity sold and decreasing prices. has no impact on the market. C D B.
- 2. Is there any dominated strategy in the following table. If there is or not explain you answer in detail. Find all Nash cquilibrium. Draw best response graphs according to beliefs. Center Right 5, 4 8, 7 Left 6,5 Up Middle 6, 3 4, 2 4,4 Down 3,5 2,7 7,65. 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.3) Consider the following two extensive form games and answer the following questions. How many subgames present in the following games? Find all pure strategies SPNE. Find all pure strategies NE of these games. Game A Game B u (5,3) u (0,2) 2 2 L L (-5,4) d (0,0) 1 1 1 (1,-5) (-10,-10) u R (2,3) A M 2 R 2 r d 1 (8,1) B (2,0) (2,2)