Consider a Variant of the ultimatum game we studied in class in which players have Fairness considerations. The timing of the game is usual. First, Player 1 proposes the split (100-X, X) OF a hundred dollars to player 2, where XE [0,100]. Player 2 observes split & decides whether to accept (in which case they recieve money according to proposed Split) or reject (in which case they both get žero dollars). But now player i's utility equals to her monetary Utility minus

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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Consider a Variant oF the uitimatum qame we Studicd inclasS
in which players have Fairness considerations. The timing
OF the qame is vsual. First , Player 1 propasar the split
(100 -x, x)
XE [0,100]. Player 2 observes split & decides whether to accept
(in which case they recieve Moncy according proposed Split)
or reject (in Which case they both get žero dollars).But
now player i's utility equals to her monetary Vtility minus
the disutility From unFairneas proportion al to the diFfrene
in Monetary outCOMES . That is, given a final Split (m. ,m.) let
OF a hundred dollars to player 2,Where
u, (m. ,m.) = m, -B. (m, - m2)*
Ui (m.,m.)
= m, - P. (m, -m.)
Where Pi,Pz are parametens of the game indicating haw strongly
Players care a bout Fairness. Noté that the case we
Considered corres pands
to B, = Bz =0
Let B,=0
7,
10
(a) Which oFFes will player 2.derinitely
allept ? revect ? Describe all sequentially rational Strategies
For player 2.
(b) For cach seqventialy ratianal Strategy
of player 2 you identiFied in part (a) ,tither describe
Whi ch proposal Maxi mizer player 1's continuation
valve or explain Why it does not exist
C pescribe alI SPNE'OF+he
game.
Transcribed Image Text:Consider a Variant oF the uitimatum qame we Studicd inclasS in which players have Fairness considerations. The timing OF the qame is vsual. First , Player 1 propasar the split (100 -x, x) XE [0,100]. Player 2 observes split & decides whether to accept (in which case they recieve Moncy according proposed Split) or reject (in Which case they both get žero dollars).But now player i's utility equals to her monetary Vtility minus the disutility From unFairneas proportion al to the diFfrene in Monetary outCOMES . That is, given a final Split (m. ,m.) let OF a hundred dollars to player 2,Where u, (m. ,m.) = m, -B. (m, - m2)* Ui (m.,m.) = m, - P. (m, -m.) Where Pi,Pz are parametens of the game indicating haw strongly Players care a bout Fairness. Noté that the case we Considered corres pands to B, = Bz =0 Let B,=0 7, 10 (a) Which oFFes will player 2.derinitely allept ? revect ? Describe all sequentially rational Strategies For player 2. (b) For cach seqventialy ratianal Strategy of player 2 you identiFied in part (a) ,tither describe Whi ch proposal Maxi mizer player 1's continuation valve or explain Why it does not exist C pescribe alI SPNE'OF+he game.
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