Consider the following perfect information sequential move game between Player 1 and Player 2, where x is an integer. Player 1 is the leader and moves first, while Player 2 is the follower and moves second, after observing Player 1's move. C N D E B 2 F

Question > Consider the following matrix game where Player 1 moves first then Player 2 observes player 1's move and responds. Draw the game tree for the sequential move game and then determine all the Nash equilibria. Player 1 Strategy A Strategy B Strategy C Strategy D -3, -2 10, 12 9, 20 Player 2 Please show each step on how to get the answer. Thank you! Strategy E 13,7 17, 17 12, 21 Strategy F 20,8 22, 16 19, 19

the Consider a simultaneous-move integer game between two players: Marilyn and Noah. Each of player is required to announce a positive integer between 1 to 4. In other words, a player can announce 1, 2, 3, or 4. Two players announce their integers simultaneously. Notice that this game is different from the games we learned in class in that each player has four actions to take. The payoffs of the players in the game are specified as follows: (1) when the two announced integers are different, whoever reports the lower number pays $1 to the other player, so that the loser of the game has payoff -1 and the winner of the game has payoff 1; (2) when the two players announce the same integer, their payoffs are both O. What is Marilyn's maximin strategy? 01 02 03 O

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= a) Suppose x 4 and y = 3. After all strategies that are dominated by a pure strategy are iteratively deleted for both players, how many strategies remain for Player 1? b) Suppose x = 4 and y = 3. After all strategies that are dominated by a pure strategy are iteratively deleted for both players, how many strategies remain for Player 2? c) Suppose x = 4 and y = 3. What is the sum of both players' payoffs in all pure strategy Nash equilibria of the game? d) Suppose x = 4 and y = 11. After all strategies that are dominated by a pure strategy are iteratively deleted for both players, how many strategies remain for Player 1? e) Suppose x = 4 and y = 11. After all strategies that are dominated by a pure strategy are iteratively deleted for both players, how many strategies remain for Player 2? f) Suppose x = 4 and y = 11. What is the sum of both players' payoffs in all pure strategy Nash equilibria of the game?

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