Exercise 1.4. There are two players. Each player is given an unmarked envelope and asked to put in it either nothing or $300 of his own money or $600. A referee collects the envelopes, opens them, gathers all the money, then adds 50% of that amount (using his own money) and divides the total into two equal parts which he then distributes to the players. (a) Represent this game frame with two alternative tables: the first table showing in each cell the amount of money distributed to Player 1 and the amount of money distributed to Player 2, the second table showing the change in wealth of each player (money received minus contribution). (b) Suppose that Player 1 has some animosity towards the referee and ranks the outcomes in terms of how much money the referee loses (the more, the better), while Player 2 is selfish and greedy and ranks the outcomes in terms of her own net gain. Represent the corresponding game using a table. (c) Is there a strict dominant-strategy equilibrium?
Exercise 1.4. There are two players. Each player is given an unmarked envelope and asked to put in it either nothing or $300 of his own money or $600. A referee collects the envelopes, opens them, gathers all the money, then adds 50% of that amount (using his own money) and divides the total into two equal parts which he then distributes to the players. (a) Represent this game frame with two alternative tables: the first table showing in each cell the amount of money distributed to Player 1 and the amount of money distributed to Player 2, the second table showing the change in wealth of each player (money received minus contribution). (b) Suppose that Player 1 has some animosity towards the referee and ranks the outcomes in terms of how much money the referee loses (the more, the better), while Player 2 is selfish and greedy and ranks the outcomes in terms of her own net gain. Represent the corresponding game using a table. (c) Is there a strict dominant-strategy equilibrium?
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.3P
Question
![Exercise 1.4. There are two players. Each player is given an unmarked envelope
and asked to put in it either nothing or $300 of his own money or $600. A referee
collects the envelopes, opens them, gathers all the money, then adds 50% of that
amount (using his own money) and divides the total into two equal parts which he
then distributes to the players.
(a) Represent this game frame with two alternative tables: the first table showing in
each cell the amount of money distributed to Player 1 and the amount of
money distributed to Player 2, the second table showing the change in wealth of
each player (money received minus contribution).
(b) Suppose that Player 1 has some animosity towards the referee and ranks the
outcomes in terms of how much money the referee loses (the more, the better),
while Player 2 is selfish and greedy and ranks the outcomes in terms of her own
net gain. Represent the corresponding game using a table.
(c) Is there a strict dominant-strategy equilibrium?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F833227fa-6456-4698-8430-712200a97c6f%2Fe9c44331-6bfc-4276-816c-064e33d47e27%2F068ymcu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Exercise 1.4. There are two players. Each player is given an unmarked envelope
and asked to put in it either nothing or $300 of his own money or $600. A referee
collects the envelopes, opens them, gathers all the money, then adds 50% of that
amount (using his own money) and divides the total into two equal parts which he
then distributes to the players.
(a) Represent this game frame with two alternative tables: the first table showing in
each cell the amount of money distributed to Player 1 and the amount of
money distributed to Player 2, the second table showing the change in wealth of
each player (money received minus contribution).
(b) Suppose that Player 1 has some animosity towards the referee and ranks the
outcomes in terms of how much money the referee loses (the more, the better),
while Player 2 is selfish and greedy and ranks the outcomes in terms of her own
net gain. Represent the corresponding game using a table.
(c) Is there a strict dominant-strategy equilibrium?
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