Amir and Beatrice play the following game. Amir offers an amount of money x = [0, 1] to Beatrice. Beatrice can either accept or reject. If Beatrice accepts, then Amir receives 1 - x dollars and Beatrice receives a dollars. If Beatrice rejects, then both receive no money. As in the Ultimatum Game, Amir cares only about maximizing the amount of money he receives. Beatrice, on the other hand, detests Amir, and therefore cares about the amount of money that both receive: if Amir receives y dollars and Beatrice receives a dollars, then Beatrice's ay where a > 0. payoff is a -
Amir and Beatrice play the following game. Amir offers an amount of money x = [0, 1] to Beatrice. Beatrice can either accept or reject. If Beatrice accepts, then Amir receives 1 - x dollars and Beatrice receives a dollars. If Beatrice rejects, then both receive no money. As in the Ultimatum Game, Amir cares only about maximizing the amount of money he receives. Beatrice, on the other hand, detests Amir, and therefore cares about the amount of money that both receive: if Amir receives y dollars and Beatrice receives a dollars, then Beatrice's ay where a > 0. payoff is a -
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.7P
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please only do: if you can teach explain each part
![Amir and Beatrice play the following game. Amir offers an amount of money x = [0, 1] to
Beatrice. Beatrice can either accept or reject. If Beatrice accepts, then Amir receives 1 - X
dollars and Beatrice receives a dollars. If Beatrice rejects, then both receive no money. As in
the Ultimatum Game, Amir cares only about maximizing the amount of money he receives.
Beatrice, on the other hand, detests Amir, and therefore cares about the amount of money
that both receive: if Amir receives y dollars and Beatrice receives x dollars, then Beatrice's
payoff is x - ay where a > 0.
(a) Find all pure strategy Nash equilibria of the game in which the two players choose
simultaneously (thus Beatrice accepts or rejects without seeing Amir's offer).
(b) Find all subgame perfect equilibria of the sequential game in which Amir first makes the
offer and Beatrice observes the offer before choosing whether to accept or reject.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa1ab2968-d288-4fd8-b87c-74963c459231%2F7f50dc50-bee9-42e4-b99a-863c013f4f8c%2F8abis2_processed.png&w=3840&q=75)
Transcribed Image Text:Amir and Beatrice play the following game. Amir offers an amount of money x = [0, 1] to
Beatrice. Beatrice can either accept or reject. If Beatrice accepts, then Amir receives 1 - X
dollars and Beatrice receives a dollars. If Beatrice rejects, then both receive no money. As in
the Ultimatum Game, Amir cares only about maximizing the amount of money he receives.
Beatrice, on the other hand, detests Amir, and therefore cares about the amount of money
that both receive: if Amir receives y dollars and Beatrice receives x dollars, then Beatrice's
payoff is x - ay where a > 0.
(a) Find all pure strategy Nash equilibria of the game in which the two players choose
simultaneously (thus Beatrice accepts or rejects without seeing Amir's offer).
(b) Find all subgame perfect equilibria of the sequential game in which Amir first makes the
offer and Beatrice observes the offer before choosing whether to accept or reject.
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