Assume a simultaneous-move game. Firm B Low Price High Price Firm A Low Price 10,10 100,2 High Price 2,100 90, 90 What is the Nash equilibrium of the game?
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Assume a simultaneous-move game.
|
Firm B |
|||
|
Low Price |
High Price |
||
|
Firm A |
Low Price |
10,10 |
100,2 |
|
High Price |
2,100 |
90, 90 |
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Solved in 2 steps
- 1. Find all subgame perfect nash equilibrium 2. Find a nash equilibrium that is not SPNE, and explain why it is not an SPNE.A B 2 2 C 3,2 D 2,1 E 1,1 F In this game, the strategy profile (B.CE) is 4 2.2 not a Nash equilibrium a subgame imperfect Nash equilibrium a subgame perfect Nash equilibriumConsider the following price game: Firm 1 Firm 2 High Low High 20, 20 12, 24 Low 24, 12 14, 14 Remark: In simultaneous move games (games with rows and columns) theconvention is to write the row player’s payoff first and the column player’spayoff second. (a) What is the Nash equilibrium of this game? Recall that for each playeryou should find the best response to each of the opponents’ strategies andunderline the associated payoff. Then look for a cell where both strategiesare best responses to each other. This is a Nash equilibrium. (b) Does either firm have a dominate strategy (a strategy that is always abest response)?
- 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…Problem Consider the following finitely repeated date game. Write down a subgame perfect equilibrium. You can do this using informal descriptions of the strategies. Iya Froyo Iva Is Frou Froyo 0,0 6,1 1,5 0,01. 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 3,3
- 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 strategiesConsider the following classic game, called Hawk and Dove. Player 2 Hawk Dove Hewk 0,0 4,1 Player 1 Dove 1,4 33 Select all pure strategy Nash equilibria and check the corresponding option if you think there exists a mixed strategy Nash equilibrium too. O There exists also a mixed strategy Nash equilibrium OHawk, Dove ODove, Hawk O Hawk, Hawk O Hawk, HawkUofC Aggressive Restrained Aggressive 18, 26 29,47 MRU Restrained 45, 59 32, 23 Consider the case of a Sequential-Move game. Uofc moves First Part 1. Is UofC 's sub-game Perfect Nash Equilibrium strategy Aggressive or Restrained? (Answer 1 for aggressive and 2 for Restrained) 1 Part 2. Is MRU's sub-game Perfect Nash Equilibrium strategy Aggressive or Restrained? (Answer 1 for aggressive and 2 for Restrained) Number: Part 3. How much profit does UofC make under the Sub-game perfect Nash-Equilibrium? Number Part 4. How much profit does MRU make under the Sub-game perfect Nash-Equilibrium? Number
- 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.What are the subgames in the following game ? find all the SPNEa)Find the Nash equilibrium b)Find subgame Nash equilibrium c) Explain why all Nash equilibrium are not subgame perfect. Please see the image The term in image are A,B b,c and w,a and 1,2,7,9 and 7,3,4,8
