uestion 1 hat differentiates a Subgame Perfect Nash Equilibrium from a Nash Equilibrium? A Subgame Perfect Nash Equilibrium requires that play in every subgame be perfectly informed, which Nash Equilibrium does not. A Subgame Perfect Nash Equilibrium requires every that play in every subgame conform to a Nash Equilibrium. Nash Equilibrium itself does not. Nash Equilibrium can involve mixed strategies, and a Subgame Perfect Nash Equilibrium cannot. A Nash Equilibrium cannot contain incredible threats, but a Subgame Perfect Nash Equilibrium can. Nash Equilibrium is only for strategic games. Subgame Perfect Nash Equilibrium is only for extensive form games. estion 2 hat are the necessary components of a strategic game? The matrix, the payoffs in each cell, the strategies. The players and their strategy sets. The players, their strategy sets, and the payoff functions for each player. The players, the game, and the equipment of their official sponsor Reebok "[slogan slogan slogan Reebok has a slogan]."

uestion 1 hat differentiates a Subgame Perfect Nash Equilibrium from a Nash Equilibrium? A Subgame Perfect Nash Equilibrium requires that play in every subgame be perfectly informed, which Nash Equilibrium does not. A Subgame Perfect Nash Equilibrium requires every that play in every subgame conform to a Nash Equilibrium. Nash Equilibrium itself does not. Nash Equilibrium can involve mixed strategies, and a Subgame Perfect Nash Equilibrium cannot. A Nash Equilibrium cannot contain incredible threats, but a Subgame Perfect Nash Equilibrium can. Nash Equilibrium is only for strategic games. Subgame Perfect Nash Equilibrium is only for extensive form games. estion 2 hat are the necessary components of a strategic game? The matrix, the payoffs in each cell, the strategies. The players and their strategy sets. The players, their strategy sets, and the payoff functions for each player. The players, the game, and the equipment of their official sponsor Reebok "[slogan slogan slogan Reebok has a slogan]."

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.9P

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Which of the following statements is true? O If a strategy is weakly dominant, then it is also strictly dominant. O None of the other answers is correct. O Games with strictly dominant strategies guarantee that players achieve the highest available payoffs in Nash Equilibrium. OIf a two-player game has a strictly dominant strategy for one player, then it does not necessarily have a strictly dominant strategy for the other player. O The prisoners' dilemma game has no strictly dominant strategy.
Which of the following statements about Nash Equilibria in a two-player one-shot simultaneous game is FALSE? O If one player has a dominant strategy, a Nash Equilibrium is guaranteed. O If both players have a dominant strategy, a Nash Equilibrium is guaranteed. O A Nash Equilibrium is conditional on at least one player having a dominant strategy. O It is possible for a game in pure strategies to not have a Nash Equilibrium. It is possible for a two-person game to have more than two Nash Equilibria.
A Nash equilibrium occurs when O no player has an incentive to unilaterally change strategies. each player has an incentive to unilaterally change strategies. O both players can cooperate to increase their payoffs. O no player can earn a higher payoff from any other strategy.
Which of the following statements is false? O A set of strategies constitute a Nash equilibrium if, given the strategies of the other players, no player can improve her payoff by unilaterally changing her own strategy. Nash equilibrium is a strategy that always results in the maximum possible payoff at least for one player. Dominant strategy is a strategy that results in the highest payoff to a player regardless of the other player's action. O Astrategy is a complete plan for playing the game, for any one of the players.
Consider the payoff matrix at right. O A. The pair of strategies high output -high output is the only Nash equilibrium. OB. The pair of strategies high output -high output and high output - low output are the only Nash equilibria. OC. The pair of strategies low output - low output and low output -high output are the only Nash equilibrium. O D. The pair of strategies low output-low output is the only Nash equilibrium. O E. The pair of strategies high output -high output and low output - low output are the only Nash equilibria. Firm A Firm B High Output Low Output High Outpu $20 $20 $28 $6 Low Output $6) $28 ($24 $24
Which of the following is the best definition for a Nash Equilbirium? * Neither player has an incentive to switch his or her strategy even if the other perso switches his or her play O The same as a Prisoner's Dilemma O Something you will choose no matter what the other person chooses The idea that no matter what people will be selfish in order to sabotage his or her opponent.
2. Consider a game that game theory people refer to as the “ultimatum game.”We will refer to our two players as the “offerer” and the “decider”. How the gameworks is that the offerer proposes a way to split $1000 between the two players.While this could be done in a variety of ways, we will assume that the offerersonly has two possible proposals: Either a 50-50 split, or she offers the decider$50 and keeps the rest. The decider can either accept or reject the offer. If the offer is accepted, the money is split as proposed. If the offer is rejected, themoney spontaneously combusts and nobody gets anything. a) List the strategies for each player and write an extensive form version of thegame with payouts. b) List all the Nash equilibria of this game. c) Explain which, if any of the Nash equilibrium are not sub-game perfect. d) Write the game out in normal form and find the pure strategy Nashequilibrium. Explain how this matches with your answers to (b) and (c) . Alsoexplain why there…
Player 1 Cooperate (C) Defect (D) 0 1 O O 1.5 Cooperate (C) 3,3 8,0 3 O 6 Player 2 If the game is repeated finitely many times, what happens in the last period in Nash equilibrium? Both players choose C. Player 1 chooses C, Player 2 chooses D. Player 1 chooses D, Player 2 chooses C. Both players choose D. Defect (D) 0,8 1,1 If the game is repeated infinitely many times, what is the value of 1's future payoffs when both cooperate forever? Assume that the discount factor is 0.5 (i.e. payoffs in the next period are worth half as much as payoffs today).
Consider the following game: A High price Low price High price Low price High price Low price Firm A O b. Firm A: high price, Firm B: high price O C. Firm A: low price, Firm B: high price O d. Firm A: high price, Firm B: low price $100 $130 $180 $150 Firm B $100 $50 $80 $120 The matrix above represents the decisions and payoffs to Firm A and Firm B. What is the solution to this game or what is the most likely outcome of this game? a. Firm A: low price, Firm B: low price
age Which of the following statements is the best description of a Nash equilibrium? Select one: O a. An equilibrium outcome achieved by cooperation between players in the game b. An outcome that is achieved when players in the game have jointly maximized profits and divided those profits according to market share of each player O c. An outcome where each player's strategy depends on the behaviour of its opponents d. An outcome where each player's best strategy is to maintain its present behaviour given the present behaviour of the other players Next page
Question 28 Suppose the following game: I Player 1 nice nice Player 2 50, 50 mean 90,20 Which of the following is true? mean 20,90 30, 30 O Both players play "mean" with a 70 % chance, and "nice" with a 30% chance. O There is no Nash Equilibrium in pure strategies, there is only one Nash Equilibrium in mixed strategies. Both players play "nice" with a 70% chance, and "mean" with a 30% chance. There is no Nash Equilibrium in mixed strategies, there is only one Nash Equilibrium in pure strategies.
Which of the following accurately describes a player's strictly dominant strategy? O It is a strategy that is better than all the player's other strategies, no matter what the other players do. There is always at least one player who has one in every game.. O It is the strategy a player uses in the Nash equilibrium of a game. Since a Nash equilibrium always exists, players always have a strictly dominant strategy. O It is a strategy that is better than all the player's other strategies, no matter what the other players do. A player may or may not have one. O It is a strategy that is better than all the player's other strategies, no matter what the other players do. Every player has a dominant strategy in every game.. O It is the strategy a player uses in the Nash equilibrium of a game. Since a Nash equilibrium may not exist, players may not always have a strictly dominant strategy.