Consider a Variant oF the utimatum qame we Studicd in class IN which playcrs have Fairness considerations . The timing OF the qame is vsual. First , Player 1 propasar the split (100 -x, x) OF a hundred dollars to Player 2, Where XE [0,100]. Player 2 observes split & decides whtther to accept (in which case they recieve Money according ti proposed Split) or reject (in Which case they both get żero dollars).But now player i's vtility equals to her monetary Vility minus the disutility From unFairneus proportion al to the diFferene in Monetary OtcCOMES . That is, given a final Split (m. ,m.) let u, (m. ,m.) = m, -B. (m, - m2)* -B. (m, - ma)* = M, U. (m. ,m,) = m, - P. (m. -m.) where P..f2 are parametens of the indicating haw strongly Players care a bout Fairness. Note that the case we considered corres pands to game o P, = P2 = 0 %3D (a) represent this game in Exten sive Form (b) Describe the sets of Strateqies oF each player
Consider a Variant oF the utimatum qame we Studicd in class IN which playcrs have Fairness considerations . The timing OF the qame is vsual. First , Player 1 propasar the split (100 -x, x) OF a hundred dollars to Player 2, Where XE [0,100]. Player 2 observes split & decides whtther to accept (in which case they recieve Money according ti proposed Split) or reject (in Which case they both get żero dollars).But now player i's vtility equals to her monetary Vility minus the disutility From unFairneus proportion al to the diFferene in Monetary OtcCOMES . That is, given a final Split (m. ,m.) let u, (m. ,m.) = m, -B. (m, - m2)* -B. (m, - ma)* = M, U. (m. ,m,) = m, - P. (m. -m.) where P..f2 are parametens of the indicating haw strongly Players care a bout Fairness. Note that the case we considered corres pands to game o P, = P2 = 0 %3D (a) represent this game in Exten sive Form (b) Describe the sets of Strateqies oF each player
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.7P
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