Consider a Variant aF the uitimatum qame we Studicd incllassin which playcrs have Fairness considerations. The timingOF the qame is usual. First , Player 1 propase the split(100 -X", x) OF a hundred dallars to player 2,WhereX E [0,100]. Player 2 observes split & decides whether to accept(in which case they recieve Money accor ding t1 proposed Split)or reject (in Which case they both get žero dollars).Butnow player i's Utility equals to her monetary Vtility minusthe disutility From unFairneas proportional to the differenein Monetary OutCOMeS . That is, given a final Split (m. ,m.) Ietu, (m. ,m.) = m, -B. (m, - m2)U, (m. ,m,) = m, - P. (m, -m.)Where Pi,ßz are parametens oF the game indicating how stronglyPlayers care a bout Fairness. Note that the case weConsidered corres ponds to B, = P2 = 0(a) represent this game in Exten siye formb) Describe the Gets of Strategies 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

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

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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3. Find ALL Nash equilibria of the following game: Nature begins by choosing one of the 2x2 games. It chooses the left game with probability a, and the right game with probability 1- a. Player 2 is INFORMED about nature's choice but player 1 IS NOT informed. L KR R 0,0| 5, 0,0 U 2, 2 0, 3 U D 3, 1, 1 D 1 Are there values of a for which there exists a mixed strategytequilibrium?
[Adverse Selection] Each of the two players receives an envelope, in which there is anamount of money that is equally distributed from $0, $1, $2, ..., $100. The amounts in twoenvelopes are independent. After receiving the envelope, each individual can check exactlyhow much money is put in his/her own envelope. Then each player has the option to exchangehis/her envelope for the other individual's prize. The decisions are made simultaneously. Ifboth individuals agree to exchange, then the envelopes are exchanged; otherwise, if at leastone player chooses not to exchange, each individual keeps his/her own envelope and receivesits attached sum of money.a. Model this game as a static Bayesian game (write the normal formrepresentation) and find the Bayesian Nash equilibrium.b. Consider a new game where the probability distribution of money in eachenvelope is changed. The amount is equal to $100 with probability 90%, and is equalto each number in $0, $1, $2, ... ,$99 with probability 0.1%.…
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Find all NE of the stage game.(b) Consider a two-period game without discounting in which the stage game is played ineach period. Find all pure strategy SPNE.(c) What’s the min-max payoff of each player?(c1) Consider pure strategies only.(c2) Consider all strategies, including the mixed ones.(d) Now suppose the stage game is repeated infinitely many times. Use the Fudenberg-Maskin Folk theorem to find all possible values of payoff that can be supported as aSPNE.
B's profit B invests B does not invest 100 80 100 -40 -40 10 80 10 Which of the following statements are correct? Select one or more: O a. If A invests, B's best strategy is to not invest since A will take all the profit O b. Whoever invests first gains a first-mover advantage O c. The co-ordination game exhibits two Nash equilibria. O d. If B chooses to not invest, A's best strategy is also to not invest. A's profit A does not invest A invests
Please give me proper calculation and full explanation otherwose i give multiple downvote Note:- Please avoid using ChatGPT and refrain from providing handwritten solutions; otherwise, I will definitely give a downvote. Also, be mindful of plagiarism. Answer completely and accurate answer. Rest assured, you will receive an upvote if the answer is accurate.
2. Consider the following two player game in normal form: Player 2 R 0, 5 2, 3 2, 3 Player 1 M 2, 3 0, 5 3, 2 B 5,0 3, 2 2, 3 (a) Show that for Player 1, strategy T is strictly dominated by a mixed strategy in which actions M and B are played with positive probability. (b) Find a mixed strategy Nash equilibrium of this game. 352
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1. Use the following game tree to answer parts a & b. At a chance node (Nature's turn) or when a player is indifferent between strategies, each branch has equal likelihood (50% chance they take either path). Nature receives no payoff. Assume players are mistake proof. Use a complete strategy when discussing the results of this game and provide a payoff, even if that payoff is an expected one. Recall that an expected payoff is the "average" payoff: for example if with 50% chance we receive a payoff of 5 and with 50% chance we receive a payoff of 2, the expected payoff is .5 x 5+ .5 x 2 = 3.5 a. What is the outcome of the game? Assume players are risk neutral (i.e., they see no difference in getting a payoff of 5 vs an expected payoff of 5). Red 0, 1, 3, 3 3, 2, 3, 2 Dorothy Blue Top 1, 4, 3, 2 Scarecrow 50% Green Nature Right Bottom 0, 2, 3, 1 Lion 50% 1, 3, 4, 2 3, 4, 3, 2 50% Left Nature 3, 2, 1, 2 Up 50% Red. 1, 3, 4, 2 Down Tinman Blue 0, 3, 3, 3 Yellow Dorothy 4, 3, 4, 2…
O 2: 12 O 6; 5 O 3:6 Support O 10; 4 (2, 12) Agree BO Disagree Not Support (6,5) (3,6) Co Not In this extensive form game between player A and B, in the subgame perfect NE, player A gets and B gets. (10,4)
3. Repeated Game Consider the game in which the stage game depicted below is infinitely repeated and in which both players discount future payoffs with discount factor 6 € [0, 1]. Player 1 E S Player 2 E 3,3 4, -1 S -1.4 1,1 (a) Suppose that both players play the tit-for-tat strategy. This strategy is characterized by exerting effort (playing E) in the first round. Then in future rounds, a player copies the action chosen by his opponent in the previous period (i.e if Player 2 shirks (plays S) in period 2, then Player 1 plays S in period 3). Then, for what values of d can tit-for-tat be supported on the equilibrium path of play? (b) Suppose that both players play the perfect tit-for-tat strategy. This strategy is characterized by exerting effort (playing E) in the first round. Then in future rounds, a player plays E unless the actions are disagreed in the previous period. Then, for what values of d can perfect tit-for-tat be supported on the equilibrium path of play?
1- Determine the strategies that the player can follow by applying the rule of thumb to reduce the matrix (2x2)2- Find the value of the match by the analytical method.