2. Suppose that Ann and Bob play a two-person game with payoffs A (for Ann) and CB (for Bob). Bob's utility is UB (XA, XB) = XB o max{2B – £A;0} − pmax{2A – TB;0} (a) Describe Bob's utility function. Explain the meaning of the two parameters p and o, and why they might differ. Do you think that it is more natural for p to be larger than o or not, and why? J (b) Ann and Bob play an ultimatum bargaining game: Bob has an endowment of 10 experimental unit and he has to decide how many experimental unit he would like to assign to Ann. Ann can either accept or reject. If she accepts, then the allocation that Bob proposes is implemented; if she rejects they both get zero and the game is over. i. Explain what is the likely outcome of this game if Ann and Bob have selfish preferences. ii. Explain how the outcome may differ if Bob is inequity averse and Ann is selfish. iii. Now assume, for simplicity, that Bob has only two possibilities: he either offers an equal split, or he keeps all the experimental units for himself. By using the utility function in (a) above, under which conditions on o and p will Bob offer an equal split? iv. Assume now that Bob is selfish and Ann is inequity averse, with prefer- ences: UACA,®B)=A- ơ max{2A – £B;0} − pmax{TB – 4;0} Show under which conditions on o and p, a selfish Bob may find it optimal to offer an equal split to an inequity averse Ann.. (c) Briefly summarise the existing experimental evidence on the ultimatum bar- gaining game.
2. Suppose that Ann and Bob play a two-person game with payoffs A (for Ann) and CB (for Bob). Bob's utility is UB (XA, XB) = XB o max{2B – £A;0} − pmax{2A – TB;0} (a) Describe Bob's utility function. Explain the meaning of the two parameters p and o, and why they might differ. Do you think that it is more natural for p to be larger than o or not, and why? J (b) Ann and Bob play an ultimatum bargaining game: Bob has an endowment of 10 experimental unit and he has to decide how many experimental unit he would like to assign to Ann. Ann can either accept or reject. If she accepts, then the allocation that Bob proposes is implemented; if she rejects they both get zero and the game is over. i. Explain what is the likely outcome of this game if Ann and Bob have selfish preferences. ii. Explain how the outcome may differ if Bob is inequity averse and Ann is selfish. iii. Now assume, for simplicity, that Bob has only two possibilities: he either offers an equal split, or he keeps all the experimental units for himself. By using the utility function in (a) above, under which conditions on o and p will Bob offer an equal split? iv. Assume now that Bob is selfish and Ann is inequity averse, with prefer- ences: UACA,®B)=A- ơ max{2A – £B;0} − pmax{TB – 4;0} Show under which conditions on o and p, a selfish Bob may find it optimal to offer an equal split to an inequity averse Ann.. (c) Briefly summarise the existing experimental evidence on the ultimatum bar- gaining game.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
Transcribed Image Text:2. Suppose that Ann and Bob play a two-person game with payoffs A (for Ann) and
CB (for Bob). Bob's utility is
UB (XA, XB) = XB o max{2B – £A;0} − pmax{2A – TB;0}
(a) Describe Bob's utility function. Explain the meaning of the two parameters p
and o, and why they might differ. Do you think that it is more natural for p
to be larger than o or not, and why?
J
(b) Ann and Bob play an ultimatum bargaining game: Bob has an endowment
of 10 experimental unit and he has to decide how many experimental unit he
would like to assign to Ann. Ann can either accept or reject. If she accepts,
then the allocation that Bob proposes is implemented; if she rejects they both
get zero and the game is over.
i. Explain what is the likely outcome of this game if Ann and Bob have selfish
preferences.
ii. Explain how the outcome may differ if Bob is inequity averse and Ann is
selfish.
iii. Now assume, for simplicity, that Bob has only two possibilities: he either
offers an equal split, or he keeps all the experimental units for himself. By
using the utility function in (a) above, under which conditions on o and p
will Bob offer an equal split?
iv. Assume now that Bob is selfish and Ann is inequity averse, with prefer-
ences:
UACA,®B)=A- ơ max{2A – £B;0} − pmax{TB – 4;0}
Show under which conditions on o and p, a selfish Bob may find it optimal
to offer an equal split to an inequity averse Ann..
(c) Briefly summarise the existing experimental evidence on the ultimatum bar-
gaining game.
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