5. Consider a game in which two players, Fred and Barney, take turns removing matchsticks from a pile. They start with 21 matchsticks, and Fred goes first. On each turn, each player may remove either 1, 2, 3, or 4 matchsticks. The player to remove the last matchstick wins the game. 1. Suppose there are only 6 matchsticks left, and it is Barney's turn. What move should Barney make to guarantee himself victory? Explain your reasoning. 2. Suppose there are 12 matchsticks left, and it is Barney's turn. What move should Barney make to guarantee himself victory? (Hint: Use your answer to part (a) and roll back.) 3. Now start from the beginning of the game. If both players play optimally, who will win?

5. Consider a game in which two players, Fred and Barney, take turns removing matchsticks from a pile. They start with 21 matchsticks, and Fred goes first. On each turn, each player may remove either 1, 2, 3, or 4 matchsticks. The player to remove the last matchstick wins the game. 1. Suppose there are only 6 matchsticks left, and it is Barney's turn. What move should Barney make to guarantee himself victory? Explain your reasoning. 2. Suppose there are 12 matchsticks left, and it is Barney's turn. What move should Barney make to guarantee himself victory? (Hint: Use your answer to part (a) and roll back.) 3. Now start from the beginning of the game. If both players play optimally, who will win?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

100%

5. Consider a game in which two players, Fred and Barney, take turns
removing matchsticks from a pile. They start with 21 matchsticks, and
Fred goes first. On each turn, each player may remove either 1, 2, 3,
or 4 matchsticks. The player to remove the last matchstick wins the
game.
1. Suppose there are only 6 matchsticks left, and it is Barney' s
turn. What move should Barney make to guarantee himself victory?
Explain your reasoning.
2. Suppose there are 12 matchsticks left, and it is Barney's turn.
What move should Barney make to guarantee himself victory? (Hint:
Use your answer to part (a) and roll back.)
3. Now start from the beginning of the game. If both players play
optimally, who will win?
4. What are the optimal (complete) strategies for each player?

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