Consider the following multistage game with two stages where player 1 is the row player and...
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Consider the following multistage game with two stages where player 1 is the row player and player 2 the column player: Stage 1: A B Si= Stage 2: U D A (2, 2) (5, 0) L (6, 6) (0, 1) B (0,5) (3, 3) R (1, 0) (2, 2) (a). What are the Nash equilibria of each stage game? (b). Assuming that both agents have a common discount factor 0 ≤ ≤ 1 express the multistage game in extensive form. (c). Denote each players strategy by (al, a²(A, A), a?(A, B), a²(B, A), a²(B, B)) where a (x, y) denotes the action of player i = 1, 2 in the second stage game given that the outcome (x, y) was realized in the first stage. Suppose that the discount factor is 8 = 0. Find all subgame perfect equilibria. (d). Find a subgame perfect perfect equilibrium strategy along with the lowest value of the discount factor required in which the outcome (A, A) is played in the first stage game. (e). Can you find a subgame perfect equilibrium in which an outcome other than (A, A) or (B, B) is played in the first stage? Consider the following multistage game with two stages where player 1 is the row player and player 2 the column player: Stage 1: A B Si= Stage 2: U D A (2, 2) (5, 0) L (6, 6) (0, 1) B (0,5) (3, 3) R (1, 0) (2, 2) (a). What are the Nash equilibria of each stage game? (b). Assuming that both agents have a common discount factor 0 ≤ ≤ 1 express the multistage game in extensive form. (c). Denote each players strategy by (al, a²(A, A), a?(A, B), a²(B, A), a²(B, B)) where a (x, y) denotes the action of player i = 1, 2 in the second stage game given that the outcome (x, y) was realized in the first stage. Suppose that the discount factor is 8 = 0. Find all subgame perfect equilibria. (d). Find a subgame perfect perfect equilibrium strategy along with the lowest value of the discount factor required in which the outcome (A, A) is played in the first stage game. (e). Can you find a subgame perfect equilibrium in which an outcome other than (A, A) or (B, B) is played in the first stage?
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a Nash equilibria of each stage game Stage 1 A A with payoffs 22 is a Nash equilibrium because neither player has an incentive to deviate unilaterally B B with payoffs 33 is also a Nash equilibrium fo... View the full answer
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