Draw the tree of the game

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Problem: Two players sequentially call numbers. First, player 1 calls either 1 or 2. Then, player 2 calls a number, such that it exceeds the previous number by either 1 or 2, and so on. The winner is the player, who first calls a number 4 or 5.

Required:

Question 1: Draw the tree of the game.

Question 2: Find the set of histories of each player.

Question 3: Find the set of strategies of each player.

Question 4: Find all SPNE. Who wins this game?

Reference no: EM132421773

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