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Two players sequentially call numbers. First, player 1 calls either 1 or 2. Then, player 2...

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 Örst calls a number 4 or 5.

(a) Draw the tree of the game.

(b) Find the set of histories of each player.

(c) Find the set of strategies of each player.

(d) Find all SPNE. Who wins this game?

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