3. Two players, Amy and Beth, play the following game called "race to 50". Amy goes first, and the two players take turns choosing a number between 1 and 7. On each turn, they add a number to a running today. The player whose move brings the total to 50 wins the game. a. If both players play optimally, who will win the game? Does this game have a first-mover advantage? Explain your reasoning. b. What are the optimal strategies (complete plans of action) for each player?

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
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Two players, Amy and Beth, play the following game called "race to 50". Amy goes first, and
the two players take turns choosing a number between 1 and 7. On each turn, they add a number to a
running today. The player whose move brings the total to 50 wins the game.
a. If both players play optimally, who will win the game? Does this game have a first-mover
3.
advantage? Explain your reasoning.
b. What are the optimal strategies (complete plans of action) for each player?
Transcribed Image Text:Two players, Amy and Beth, play the following game called "race to 50". Amy goes first, and the two players take turns choosing a number between 1 and 7. On each turn, they add a number to a running today. The player whose move brings the total to 50 wins the game. a. If both players play optimally, who will win the game? Does this game have a first-mover 3. advantage? Explain your reasoning. b. What are the optimal strategies (complete plans of action) for each player?
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