In a gambling game, Player A and Player B both have a $1 and a $5 bill. Each player selects one of the bills without the other player knowing the bill selected. Simultaneously they both reveal the bills selected. If the bills do not match, Player A wins Player B's bill. If the bills match, Player B wins Player A's bill. a. Develop the game theory table for this game. The values should be expressed as the gains (or losses) for Player A. b. Is there a pure strategy? Why or why not? c. Determine the optimal strategies and the value of this game. Does the player over the other? d. Suppose Player B decides to deviate from the optimal strategy and begins playing each bill 50% of the time. What should Player A do to improve Player A’s winnings? Comment on why it is important to follow an optimal game theory strategy. game favor one

In a gambling game, Player A and Player B both have a $1 and a $5 bill. Each player selects one of the bills without the other player knowing the bill selected. Simultaneously they both reveal the bills selected. If the bills do not match, Player A wins Player B's bill. If the bills match, Player B wins Player A's bill. a. Develop the game theory table for this game. The values should be expressed as the gains (or losses) for Player A. b. Is there a pure strategy? Why or why not? c. Determine the optimal strategies and the value of this game. Does the player over the other? d. Suppose Player B decides to deviate from the optimal strategy and begins playing each bill 50% of the time. What should Player A do to improve Player A’s winnings? Comment on why it is important to follow an optimal game theory strategy. game favor one

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

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In a gambling game, Player A and Player B both have a $1 and a $5 bill. Each player
selects one of the bills without the other player knowing the bill selected. Simultaneously
they both reveal the bills selected. If the bills do not match, Player A wins Player B's bill.
If the bills match, Player B wins Player A's bill.
a. Develop the game theory table for this game. The values should be expressed as the
gains (or losses) for Player A.
b. Is there a pure strategy? Why or why not?
Determine the optimal strategies and the value of this game. Does the game favor one
player over the other?
d. Suppose Player B decides to deviate from the optimal strategy and begins playing
each bill 50% of the time. What should Player A do to improve Player A’s winnings?
Comment on why it is important to follow an optimal game theory strategy.
с.

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