Two brothers, Josh and Nathan, play a game in which actions are Left and Right. The payoff matrix is as follows. Nathan Left Right Josh Left 5,2 5,6 Right 2,4 3,6 What is the Nash equilibrium of this game? O A) (right, right) O B) This game has no Nash equilibrium. ) ( left, left) O D) (left, right)
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- GAME 5 Player B B2 B1 Player A A1 7, 3 5, 10 A2 3, 8 9, 6 In Game 5 above, O there are no Nash equilibria in pure strategies. Player A choosing A1 and Player B choosing B2 is a Nash equilibrium. O Player A choosing A1 and Player B choosing B1 is a Nash equilibrium. O Player A choosing A2 and Player B choosing B1 is a Nash equilibrium.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.Consider the following simultaneous move game: Player 1 \ Player 2 Top Bottom Select one: Left Right 5,3 4,1 2,0 0,2 Player 2 has a dominant strategy in this game. Player 1 has a dominant strategy in this game. O This game has a Nash equilibrium in dominant strategies. This game does not have a Nash equilibrium in pure strategies. None of the statements is correct. O
- Consider the following game: Player 2 In Out Player 1 In -2,-2 2, 0 Out 0, 2 0, 0 (a) What is the Nash equilibrium of this game, or what are the Nash equilibriaof this game? (b) Does either firm have a dominate strategy (a strategy that is always abest response)? Which? (c) Suppose Player 1 could move before Player 2 and Player 2 could observe Player 1’s move. What do you think would happen?GAME UUU B1 Player B B2 A1 7,13 5, 10 A2 3,8 9,16 Player A A3 5,8 4,7 In Game UUU (see table above), assuming players move simultaneously, Player A choosing A1 and Player B choosing B3 is a Nash equilibrium. Player A choosing A3 and Player B choosing B2 is a Nash equilibrium. Both Player A choosing A1 and Player B choosing B1 and Player A choosing A2 and player B choosing B2 are Nash equilibria in pure strategies Player A choosing A1 and Player B choosing B2 is a Nash equilibrium.20) Given the payoff matrix in the figure, the Nash equilibrium outcome of this game is for: Ajinomoto Produce 30 Produce 40 million pounds million pounds Ajinomoto makes $180 million Ajinomoto makes $200 million Produce 30 million ADM makes $180 million ADM makes $150 million pounds Ajinomoto makes $150 million Ajinomoto makes $160 million Produce 40 million ADM makes $200 million ADM makes $160 million pounds O A. each firm to produce 30 million pounds. B. each firm to produce 40 million pounds. C. ADM to produce 30 million pounds and for Ajinomoto to produce 40 million pounds. D. ADM to produce 40 million pounds and for Ajinomoto to produce 30 million pounds. ADM
- The following table contains the possible actions and payoffs of players 1 and 2. Player 1 U M D L 2,10 2,5 8,7 Player 2 C 5,2 11,8 8,4 R 5,4 2,9 8,3 This is a simultaneous move game. In a pure strategy Nash equilibrium of this game, Player 1 receives a payoff of ✓and player 2 receives a payoff of If, instead of playing simultaneously, player 2 moves first, then in the Nash equilibrium player 1 receives a payoff of ✓and player 2 receives a payoff ofConsider the following simultaneous game: Player 1 U D Player 2 L 20,-10 -10, 20 R -10, 20 20,-10 Please indicate whether each of the following statements is true or false. Player 1 has a dominant strategy. This game has a Nash equilibrium. This game has a Nash equilibrium in pure strategies. Player 1's best response is D if player 2 plays R.Consider 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 O Hawk, Dove O Dove, Hawk O Hawk, Hawk O Hawk, Hawk
- Which of the following statements about Nash Equilibria in a two-player one-shot simultaneous game is FALSE? 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. A Nash Equilibrium is conditional on at least one player having a dominant strategy. Click SoRefer to the accompanying figure. What is the Nash equilibrium of this game? Player A O Multiple Choice O Up O Down Player B Left 5 for A 30 for B -2 for A 10 for B A chooses Up, B chooses Right A chooses Up, B chooses Left Right 10 for A 12 for B 8 for A 15 for B A chooses Down, B chooses Right A chooses Down, B chooses LeftCostco Spend $1B on advertising Spend $1.5B on advertising Spend $1B on advertising $3.5B; $2.7B $4.2; $2.2B Target Spend $1.5B on advertising $3.2B; $3.4B $4B; $3B