Hi. I am stuck on this question for my game theory class, and was wondering if a

Question

Hi. I am stuck on this question for my game theory class, and was wondering if anyone could help me out. Additionally does this game have a first mover advantage or a second move advantage? Is there any way someone can guarantee winning this game?

Two players, Amy and Beth, play the following game with a jar containing 100 pennies. The players take turns; Amy goes first. Each time it is a player's turn, she takes between one and 10 pennies out of the jar. The player whose move empties the jar wins. If both players play optimally, who will win the game? Does this game have a first-mover advantage? Explain your reasoning. What are the optimal strategies (complete plans of action) for each player?

Explanation / Answer

a) The game has a first-mover advantage. Amy will win the game.

b) The strategy that Amy has is as follows: In the first turn Amy picks up 1 penny. Thereafter, if Beth picks up x pennies, she must pick up 11-x pennies, thus,after 9 of Beth's turns, 99 pennies would be picked up, and finallly in her 10th turn, Amy will pick up the last penny and win the game!(as a part of the last 11-x)

Beth doesn't have a winning strategy.

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