Consider a Variant aF the uitimatum qame we Studicd inclass in which players have Fairness considerations. The timing OF the qame is vsual. First , Player 1 propasas the split (100 -x, x) OF a hundred dollars to Player 2,where XE [0,100. Player 2 observes split & decides whtther to accep= in Nhich case they recieve Money accor ding ti proposed Split)

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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Consider a Variant aF the uitimatum qame we Studicd in class
in which players have Fairnes con siderations. The timing
OF the qame is vsual. First , Player 1 propaser the split
(100 -x, x) OF a hundred dallars to player 2,where
XE [0,10]. Player 2 observes split & decides whether to accept
(in which case they recieve Meney according to propased Split)
or reject (in Which case they both get žero dollars).But
noN player i's Utility cquals to her monetary Vility minus
the disutility From unFairness proportion al to the diFference
in Monttary OutcOMes . That is, given a final Split (m. ,m.) ker
u, (m, ,m.)
= m, -B. (m, - m2)*
Ui (m. ,ma) = m, - P. (m,-m.)
Where Pi ,Pz are parametens of the game indicatihg haw strongly
Players care a bout Fairness. Noté that the case we
con sidered corres pends to B, = P2 =0
(a) represent this game in Exten sive Form
(b) Describe the sets of Strategies oF each player
Transcribed Image Text:Consider a Variant aF the uitimatum qame we Studicd in class in which players have Fairnes con siderations. The timing OF the qame is vsual. First , Player 1 propaser the split (100 -x, x) OF a hundred dallars to player 2,where XE [0,10]. Player 2 observes split & decides whether to accept (in which case they recieve Meney according to propased Split) or reject (in Which case they both get žero dollars).But noN player i's Utility cquals to her monetary Vility minus the disutility From unFairness proportion al to the diFference in Monttary OutcOMes . That is, given a final Split (m. ,m.) ker u, (m, ,m.) = m, -B. (m, - m2)* Ui (m. ,ma) = m, - P. (m,-m.) Where Pi ,Pz are parametens of the game indicatihg haw strongly Players care a bout Fairness. Noté that the case we con sidered corres pends to B, = P2 =0 (a) represent this game in Exten sive Form (b) Describe the sets of Strategies oF each player
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