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In the “divide two apples” game, player 1 suggests a division scheme (x,y) from the set...

In the “divide two apples” game, player 1 suggests a division scheme (x,y) from the set {(2, 0), (1, 1), (0, 2)} where x is the number of apples allocated to player 1, and y is the number of apples allocated to player 2. Player 2 counters with a division scheme of her own that comes from the same set. The final allocation is obtained by averaging the two proposed division schemes. The apples can be cut if the resulting numbers are fractional. The payoff of each player is the number of apples (possibly fractional) he or she receives.

a) How many pure strategies does either player have?
b) Find the pure strategy subgame-perfect equilibria of this game.
c) Find all pure strategy Nash equilibria of this game that are not subgame-perfect.

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