A husband and wife would produce incomes Yh and Yw in their fallback situations. The utility each derives in any circumstance is just equal to his or her consumption expenditure in that circumstance. In their fallback situations, their consumption expenditure levels are just equal to their incomes. Thus their fallback levels of utility are Yh and Yw. If they cooperate, they produce Z>Yh + Yw. They engage in Nash cooperative bargaining to determine how to allocate Z across the consumption of the husband, Ch, and consumption of the wife, Cw, subject to the budget constraint that Ch + Cw = Z. Under any bargained allocation, the two would derive utilities of Ch and Cw. What do Ch and Cw equal if Yh = Yw (but this quantity is not equal to zero)?

A husband and wife would produce incomes Yh and Yw in their fallback situations. The utility each derives in any circumstance is just equal to his or her consumption expenditure in that circumstance. In their fallback situations, their consumption expenditure levels are just equal to their incomes. Thus their fallback levels of utility are Yh and Yw. If they cooperate, they produce Z>Yh + Yw. They engage in Nash cooperative bargaining to determine how to allocate Z across the consumption of the husband, Ch, and consumption of the wife, Cw, subject to the budget constraint that Ch + Cw = Z. Under any bargained allocation, the two would derive utilities of Ch and Cw. What do Ch and Cw equal if Yh = Yw (but this quantity is not equal to zero)?

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter15: Strategic Games

Section: Chapter Questions

Problem 15.1IP

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A husband and wife would produce incomes Yh and Yw in their fallback situations. The utility each derives in any circumstance is just equal to his or her consumption expenditure in that circumstance. In their fallback situations, their consumption expenditure levels are just equal to their incomes. Thus their fallback levels of utility are Yh and Yw. If they cooperate, they produce Z>Yh + Yw. They engage in Nash cooperative bargaining to determine how to allocate Z across the consumption of the husband, Ch, and consumption of the wife, Cw, subject to the budget constraint that Ch + Cw = Z. Under any bargained allocation, the two would derive utilities of Ch and Cw. a) The surplus associated with cooperation is S = Z − Yh − Yw. Show that each spouse consumes his or her fallback income plus half the surplus in the Nash cooperative bargaining solution. Please do fast ASAP fast please.
Mr. and Mrs. Ward typically vote oppositely in elections and so their votes “cancel each other out.” They each gain two units of utility from a vote for their positions (and lose two units of utility from a vote against their positions). However, the bother of actually voting costs each one unit of utility. Diagram a game in which they choose whether to vote or not to vote, and determine the Nash Equilibrium.
Consider the following simplified bargaining game. Players 1 and 2 have preferences over two goods, x and y. Player 1 is endowed with one unit of good x and none of good y, while Player 2 is endowed with one unit of y and none of good x. Player i has utility function: min{xi, yi} where xi is i's consumption of x and yi his consumption of y. The "bargaining" works as follows. Each player simultaneously hands any (nonnegative) quantity of the good he possesses (up to his entire endowment) to the other player. (a) Write this as a game in normal form. (b) Find all pure strategy equilibria of this game. (c) Does this game have a dominant strategy equilibrium? If so, what is it? If not, why not? Please show all work. Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.
Microsoft and a smaller rival often have to select from one of two competing technologies, A and B. The rival always prefers to select the same technology as Microsoft (because compatibility is important), while Microsoft always wants to select a different technology from its rival. If the two companies select different technologies, Microsoft's payoff is 4 units of utility, while the small rival suffers a loss of utility of 2. If the two companies select the same technology, Microsoft suffers a loss of utility of 2 while the rival gains 2 units of utility. Using the given information, fill in the payoffs for each cell in the matrix, assuming that each company chooses its technology simultaneously. Microsoft Technology A Technology B Rival Technology A Rival: , Microsoft Rival: , Microsoft Technology B Rival: , Microsoft Rival: , Microsoft True or False: There is an equilibrium for this game in pure strategies.
Consider a variant of the three player majority game we introduced in class. The three players, 1, 2, and 3, again need to decide how to allocate one unit of resources amongst themselves by voting. However, now player 1 has 1 vote, player 2 has 2 votes, and player 3 has 3 votes. To pass a proposed allocation, at least five votes are required. So, any coalition that does not possess at least five votes has only one action that gives each of its members zero resources, while any coalition that does possess at least five votes can choose any allocation of the one unit of resources amongst its members (e.g., an action of the grand coalition is simply an allocation (x1, x2, x3) such that xi ≥ 0 for all i is the portion of resources allocated to player i and x1 + x2 + x3 ≤ 1). Find the core of this game.
Microsoft and a smaller rival often have to select from one of two competing technologies, A and B. The rival always prefers to select the same technology as Microsoft (because compatibility is important), while Microsoft always wants to select a different technology from its rival. If the two companies select different technologies, Microsoft's payoff is 3 units of utility, while the small rival suffers a loss of utility of 1. If the two companies select the same technology, Microsoft suffers a loss of utility of 1 while the rival gains 1 units of utility.
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To Vote or Not to Vote Mr. and Mrs. Ward typically vote oppositely in elections and so their votes “cancel each other out.” They each gain two units of utility from a vote for their positions (and lose two units of utility from a vote against their positions). However, the bother of actually voting costs each one unit of utility. Diagram a game in which they choose whether to vote or not to vote. Mrs. Ward vote. don't vote Mr. Ward Vote. -1, -1. 1, -2 don't vote. -2, 1. 0,0?
Two roommates John and Joe are playing a simultaneous game of cleaning the apartment. If neither of them clean, the apartment gets filthy and both get a utility of 2. If John cleans and Joe doesn’t, John gets a utility of 1 and Joe gets a utility of 4. If Joe cleans and John doesn’t, Joe gets a utility of 1 and John gets a utility of 4 and if both clean up the apartment, they each get a utility of 3.What is the Nash equilibrium of this game? Group of answer choices Joe cleans, John doesn’t John cleans, Joe doesn’t Both of them clean the apartment Neither of them clean the apartment
Mr. Ward and Mrs. Ward typically vote oppositely in elections, so their votes “cancel each other out.” They each gain 10 units of utility from a vote for their positions (and lose 10 units of utility from a vote against their positions). However, the bother of actually voting costs each 5 units of utility. The following matrix summarizes the strategies for both Mr. Ward and Mrs. Ward. Using the given information, fill in the payoffs for each cell in the matrix. For example, in the top left cell, fill in the payoffs for Mr. Ward and Mrs. Ward if they both vote. (Hint: Be sure to enter a minus sign if the payoff is negative.) Mrs. Ward Vote Don't Vote Mr. Ward Vote Mr. Ward: , Mrs. Ward Mr. Ward: , Mrs. Ward Don't Vote Mr. Ward: , Mrs. Ward Mr. Ward: , Mrs. Ward
Within a voluntary contribution game, the Nash equilibrium level of contribution is zero, but in experiments, it is often possible to sustain positive levels of contribution for a long period. How might we best explain this? A) Participants are altruistic, and so value the payoff which other participants receive, benefiting (indirectly) from making a contribution. B) Participants believe that if they make a contribution, then other participants will be more likely to make a contribution. C) Participants in experiments believe that they have to make contributions in order to receive any payoff from their participation. D) Participants have experience of working in situations in which cooperation can be sustained for mutual benefit and so have internalised a social norm of cooperation
The prisoner illustrates that rational, self-interested individuals will natuarally avoid the Nash equilibrium, because it is worse for both of them, true or false and why ?