b. Now suppose that Player B has a different utility function from what wasdescribed earlier. She has two components to her utility: money and comparison.Let d = TA – TB be the difference between the two players' payoffs in the game.Then assume Player B's utility function is U(m,d) = m – 0.5d. The game stillfunctions exactly as it did before, with Player A proposing a split of the pot andPlayer B deciding to accept the proposal or reject it. Player B still gets 0 utility ifshe rejects Player A's proposal, and she still accepts a proposal if she isindifferent between accepting and rejecting. Draw a new game tree reflectingPlayer B's different utility function. What rule will Player B follow in decidingwhether to accept an offer? Knowing this, how much will Player A offer Player Bin Nash equilibrium?c. Now suppose that there are two types of people: Type I, those whose utilityfunctions are U(m) = m, and Type II, those whose utility functions are U(m,d) =m- 0.5d. Suppose everyone knows that half of the population is the first type, andhalf is the second type. Suppose Player A knows that he is Type I, but he does notknow Player B's type. What is Player A's expected utility (that is, the expectedvalue of his utility) in this case from making his proposal as if Player B wereType I and didn't care about comparison? What is his expected utility frommaking his proposal as if Player B were Type II and did care about comparison?Which proposal of those two should he make?d. What insights does this model provide about the pitfalls of designingcompensation schemes inside your firm? 3.Suppose two players, Player A and Player B, are playing a game called, "Splitthe Pot." It works like this: in front of them is a pot with $1000. Player A proposes adivision of the pot in the form of (TA, TB), where TA is the amount Player A gets to keep,TB is the amount Player B gets to keep, and TA + TB = 1000. Player B then decides toaccept or reject Player A's proposal. If Player B accepts the proposed division of the pot,then Player A gets TA, and Player B gets TB. If Player B rejects the proposed division ofthe pot, then they both get 0.Suppose that Player A's utility from an amount of money is equal to the amount ofmoney: U(m) = m. Suppose the same is true for Player B. This means that if Player Baccepts Player A's proposal, Player A's utility will be U(TA) = TA, and Player B's utilitywill be U(TB) = TB. Suppose for now that there is no other source of utility in this gamefor either player. Each player only cares about how much money he or she gets andabsolutely nothing else. Also suppose that if Player B is indifferent between accepting aproposal and rejecting it – that is, if Player B's utility from accepting a proposal isequal to her utility from rejecting it – then she will accept it.a. Draw the game tree for this sequential game. What will Player B's utility be inNash Equilibrium?b. Now suppose that Player B has a different utility function from what wasdescribed earlier. She has two components to her utility: money and comparison.Lot d-be the difforon0e hotwoon thevors' no uoff. in the

a) : The sequential game is in shown in fig 1. The nash equilibrium of the game is πA* = 1,500 and…

b. Now suppose that Player B has a different utility function from what was described earlier. She has two components to her utility: money and comparison. Let d = TA – TB be the difference between the two players' payoffs in the game. Then assume Player B's utility function is U(m,d) = m – 0.5d. The game still functions exactly as it did before, with Player A proposing a split of the pot and Player B deciding to accept the proposal or reject it. Player B still gets 0 utility if she rejects Player A's proposal, and she still accepts a proposal if she is indifferent between accepting and rejecting. Draw a new game tree reflecting Player B's different utility function. What rule will Player B follow in deciding whether to accept an offer? Knowing this, how much will Player A offer Player B in Nash equilibrium? c. Now suppose that there are two types of people: Type I, those whose utility functions are U(m) = m, and Type II, those whose utility functions are U(m,d) = m- 0.5d. Suppose everyone knows that half of the population is the first type, and half is the second type. Suppose Player A knows that he is Type I, but he does not know Player B's type. What is Player A's expected utility (that is, the expected value of his utility) in this case from making his proposal as if Player B were Type I and didn't care about comparison? What is his expected utility from making his proposal as if Player B were Type II and did care about comparison?

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...