9. Consider a Variant aF the uitimatum qame we Studicd in classin which players have Fairnes con siderations. The timingOF the qame is vsual. First , Player 1 propaser the split(100 -x, x) OF a hundred dallars to player 2,whereXE [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).ButnoN player i's Utility cquals to her monetary Vility minusthe disutility From unFairness proportion al to the diFferencein Monttary OutcOMes . That is, given a final Split (m. ,m.) keru, (m, ,m.)= m, -B. (m, - m2)*Ui (m. ,ma) = m, - P. (m,-m.)Where Pi ,Pz are parametens of the game indicatihg haw stronglyPlayers care a bout Fairness. Noté that the case wecon sidered corres pends to B, = P2 =0(a) represent this game in Exten sive Form(b) Describe the sets of Strategies oF each player

Given information Utility of player 1: u1 ( m1, m2) = m1 - β1 ( m1 - m2)2 Here β1 parameter which…

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)

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)

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter2: Mathematics For Microeconomics

Section: Chapter Questions

Problem 2.16P

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Consider a Variant oF the ultimatum 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) OF a hundred dellars to player 2,Where XE [0,100]. Player 2 observes split & decides whether to accept (in which case they recieve Money accor ding ti 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 proportional tO the differene in Monetary OutcCOMeS . That is, qiven a Final Split (m. ,m.) ket u, (m. ,m.) = m, -P. (m, - m2)" %3D U. (m. ,m2) = m,- P2 (m,-m.) Where PP are parametens of the game indicating how strongly Players care a bout Fairness. Note that the case we considered corres pends to B, = B2 = 0 (a) Let B, = To ,P2 = alcept ? revect ? Describe all seguentially rational Strategies For player 2. b) Let B, = 10 ,$=0. For each sequentially rational Strategy of player 2 yoU…
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You and a coworker are assigned a team project on which your likelihood or a promotion will be decidedon. It is now the night before the project is due and neither has yet to start it. You both want toreceive a promotion next year, but you both also want to go to your company’s holiday party that night.Each of you wants to maximize his or her own happiness (likelihood of a promotion and mingling withyour colleagues “on the company’s dime”). If you both work, you deliver an outstanding presentation.If you both go to the party, your presentation is mediocre. If one parties and the other works, yourpresentation is above average. Partying increases happiness by 25 units. Working on the project addszero units to happiness. Happiness is also affected by your chance of a promotion, which is depends on howgood your project is. An outstanding presentation gives 40 units of happiness to each of you; an aboveaverage presentation gives 30 units of happiness; a mediocre presentation gives 10 units…
a W 3,5 3,4 8,4 0,0 3,3 8,9 y 0,1 5,9 9,8 Describe a strategy for player 1 that dominates x. O (1/3.0. 2/3) 1.0,0) O01.1) to
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…
A game is played as follows: First Player 1 decides (Y or N) whether or not to play.If she chooses N, the game ends. If she chooses Y, then Player 2 decides (Y or N) whetheror not to play. If he chooses N the game ends. If he chooses Y, then they go ahead and playanother game with the payoffs shown below. A player who opts out by choosing N gets 2 andthe other player gets 0. Draw the tree of this game and then find the two subgame-perfect Nashequilibria.
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