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3. Consider a variant of the Nim game called Stones. Suppose that initially there is a single pile of 5 stones and two players, I and II. Each player takes turns picking up either 1 or 2 stones from the pile. Player I moves first, then Player II, then Player I, etc. until all stones have been picked up. Assuming that the loser is the player who picks up the last stone, write the game of Stones out in extensive (game-tree) form labeling strategies in terms of remaining stones (as in the Nim game discussed in class). Be sure to assign payoffs to the terminal nodes. a. b. Who has a winning strategy, Player I or Player II and what is it? Explain c. Redo parts a-b under the assumption that the winner is the player who picks up the last stone.

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