Players 1 and 2 are leaving the house and need to decide whether or not to bring an umbrella. They know there's a 75% chance that it will rain (thanks AccuWeather). If they don't bring an umbrella and it rains they receive a payoff of -7. If they do bring an umbrella and it rains, they receive a payoff of -4. If it doesn't rain, but they bring an umbrella they receive a payoff of -2. Finally, if it doesn't rain and they don't bring an umbrella they receive a payoff of 2. Player 1 learns the weather before they leave the house, but player 2 does not. Player 2 can, however, observe player 1s choice. (a) Represent this game in the extensive form. i. Use backwards induction to solve for the Nash equilibrium (b) Represent this game in the normal form i. Solve for the Nash equilibrium (c) Are the equilibrium strategy profiles the same in a) and b)? Explain why or why not.
Players 1 and 2 are leaving the house and need to decide whether or not to bring an umbrella. They know there's a 75% chance that it will rain (thanks AccuWeather). If they don't bring an umbrella and it rains they receive a payoff of -7. If they do bring an umbrella and it rains, they receive a payoff of -4. If it doesn't rain, but they bring an umbrella they receive a payoff of -2. Finally, if it doesn't rain and they don't bring an umbrella they receive a payoff of 2. Player 1 learns the weather before they leave the house, but player 2 does not. Player 2 can, however, observe player 1s choice. (a) Represent this game in the extensive form. i. Use backwards induction to solve for the Nash equilibrium (b) Represent this game in the normal form i. Solve for the Nash equilibrium (c) Are the equilibrium strategy profiles the same in a) and b)? Explain why or why not.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![6. Players 1 and 2 are leaving the house and need to decide whether or not to bring an umbrella.
They know there's a 75% chance that it will rain (thanks AccuWeather). If they don't bring
an umbrella and it rains they receive a payoff of -7. If they do bring an umbrella and it rains,
they receive a payoff of -4. If it doesn't rain, but they bring an umbrella they receive a payoff
of -2. Finally, if it doesn't rain and they don't bring an umbrella they receive a payoff of 2.
Player 1 learns the weather before they leave the house, but player 2 does not. Player 2 can,
however, observe player 1s choice.
(a) Represent this game in the extensive form.
i. Use backwards induction to solve for the Nash equilibrium
(b) Represent this game in the normal form
i. Solve for the Nash equilibrium
(c) Are the equilibrium strategy profiles the same in a) and b)? Explain why or why not.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F68c8d59a-da57-447f-9f0c-adb1654ae0a5%2F183bd309-e388-4aa0-8265-66d3f357af52%2Fpfx863n_processed.png&w=3840&q=75)
Transcribed Image Text:6. Players 1 and 2 are leaving the house and need to decide whether or not to bring an umbrella.
They know there's a 75% chance that it will rain (thanks AccuWeather). If they don't bring
an umbrella and it rains they receive a payoff of -7. If they do bring an umbrella and it rains,
they receive a payoff of -4. If it doesn't rain, but they bring an umbrella they receive a payoff
of -2. Finally, if it doesn't rain and they don't bring an umbrella they receive a payoff of 2.
Player 1 learns the weather before they leave the house, but player 2 does not. Player 2 can,
however, observe player 1s choice.
(a) Represent this game in the extensive form.
i. Use backwards induction to solve for the Nash equilibrium
(b) Represent this game in the normal form
i. Solve for the Nash equilibrium
(c) Are the equilibrium strategy profiles the same in a) and b)? Explain why or why not.
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