- Consider a version of the ultimatum game where the second mover is allowed to make a counter-offer: Hence, the first mover (player 1) initially proposes a division (x, 1 - x) where x = [0, 1] is the share of the pie kept by the first mover (player 1) and 1 - x the share offered to the second mover (player 2); if player 2 accepts the offer (x, 1 — x), the payoff of the player 1 is x and the payoff of the player 2 is 1 - x, and the game ends; if player 2 rejects the initial offer, he can make a counter-offer (y, 1 - y), where y = [0, 1] is the share offered to player 1, and 1 - y the share kept by player 2; if player 1 accepts the counter-offer, the payoffs are y and 1 - y accordingly, and the game ends; if player 1 rejects the counter-offer, the game ends and both players receive a payoff of (). The following graph illustrates a corresponding offer-counter-offer path: 1 8 A 2 R 2 x, 1-x Vy 1 R 0,0 A y, 1 - y Which of the following statements is NOT correct? Select one: ○ A. The game has a unique backward induction equilibrium. ○ B. A strategy of player 1 consists of an offer x, together with an Accept/Reject decision for each counter-offer y = [0, 1] that follows a rejection of an initial offer. ○ C. Every backward induction equilibrium yields a division where player 2 keeps the whole pie. ○ D. A strategy of player 2 consists of an Accept/Reject decision for each possible offer x = [0, 1] together with a counter-offer y = [0, 1] following any rejection of an initial offer x = [0,1].
- Consider a version of the ultimatum game where the second mover is allowed to make a counter-offer: Hence, the first mover (player 1) initially proposes a division (x, 1 - x) where x = [0, 1] is the share of the pie kept by the first mover (player 1) and 1 - x the share offered to the second mover (player 2); if player 2 accepts the offer (x, 1 — x), the payoff of the player 1 is x and the payoff of the player 2 is 1 - x, and the game ends; if player 2 rejects the initial offer, he can make a counter-offer (y, 1 - y), where y = [0, 1] is the share offered to player 1, and 1 - y the share kept by player 2; if player 1 accepts the counter-offer, the payoffs are y and 1 - y accordingly, and the game ends; if player 1 rejects the counter-offer, the game ends and both players receive a payoff of (). The following graph illustrates a corresponding offer-counter-offer path: 1 8 A 2 R 2 x, 1-x Vy 1 R 0,0 A y, 1 - y Which of the following statements is NOT correct? Select one: ○ A. The game has a unique backward induction equilibrium. ○ B. A strategy of player 1 consists of an offer x, together with an Accept/Reject decision for each counter-offer y = [0, 1] that follows a rejection of an initial offer. ○ C. Every backward induction equilibrium yields a division where player 2 keeps the whole pie. ○ D. A strategy of player 2 consists of an Accept/Reject decision for each possible offer x = [0, 1] together with a counter-offer y = [0, 1] following any rejection of an initial offer x = [0,1].
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.7P
Related questions
Question
not use ai please
![-
Consider a version of the ultimatum game where the second mover is allowed to make a
counter-offer: Hence, the first mover (player 1) initially proposes a division (x, 1 - x)
where x = [0, 1] is the share of the pie kept by the first mover (player 1) and 1 - x the
share offered to the second mover (player 2); if player 2 accepts the offer (x, 1 — x),
the payoff of the player 1 is x and the payoff of the player 2 is 1 - x, and the game ends;
if player 2 rejects the initial offer, he can make a counter-offer (y, 1 - y), where
y = [0, 1] is the share offered to player 1, and 1 - y the share kept by player 2; if player
1 accepts the counter-offer, the payoffs are y and 1 - y accordingly, and the game ends;
if player 1 rejects the counter-offer, the game ends and both players receive a payoff of ().
The following graph illustrates a corresponding offer-counter-offer path:
1
8
A
2
R
2
x, 1-x
Vy
1
R
0,0
A
y, 1 - y
Which of the following statements is NOT correct?
Select one:
○ A. The game has a unique backward induction equilibrium.
○ B. A strategy of player 1 consists of an offer x, together with an Accept/Reject
decision for each counter-offer y = [0, 1] that follows a rejection of an initial
offer.
○ C. Every backward induction equilibrium yields a division where player 2 keeps the
whole pie.
○ D. A strategy of player 2 consists of an Accept/Reject decision for each possible
offer x = [0, 1] together with a counter-offer y = [0, 1] following any rejection
of an initial offer x = [0,1].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe148b8fc-a13c-4cb8-a185-9e8d2e2774f5%2Ff72922a8-c1c7-4aad-8ec8-f3f8449a7029%2Fr724z4s_processed.png&w=3840&q=75)
Transcribed Image Text:-
Consider a version of the ultimatum game where the second mover is allowed to make a
counter-offer: Hence, the first mover (player 1) initially proposes a division (x, 1 - x)
where x = [0, 1] is the share of the pie kept by the first mover (player 1) and 1 - x the
share offered to the second mover (player 2); if player 2 accepts the offer (x, 1 — x),
the payoff of the player 1 is x and the payoff of the player 2 is 1 - x, and the game ends;
if player 2 rejects the initial offer, he can make a counter-offer (y, 1 - y), where
y = [0, 1] is the share offered to player 1, and 1 - y the share kept by player 2; if player
1 accepts the counter-offer, the payoffs are y and 1 - y accordingly, and the game ends;
if player 1 rejects the counter-offer, the game ends and both players receive a payoff of ().
The following graph illustrates a corresponding offer-counter-offer path:
1
8
A
2
R
2
x, 1-x
Vy
1
R
0,0
A
y, 1 - y
Which of the following statements is NOT correct?
Select one:
○ A. The game has a unique backward induction equilibrium.
○ B. A strategy of player 1 consists of an offer x, together with an Accept/Reject
decision for each counter-offer y = [0, 1] that follows a rejection of an initial
offer.
○ C. Every backward induction equilibrium yields a division where player 2 keeps the
whole pie.
○ D. A strategy of player 2 consists of an Accept/Reject decision for each possible
offer x = [0, 1] together with a counter-offer y = [0, 1] following any rejection
of an initial offer x = [0,1].
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