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Every year, management and labor renegotiate a new employment contract by sending their proposals to an arbitrator, who chooses the best proposal (effectively giving one side or the other $5 million). Each side can choose to hire, or not hire, an expensive labor lawyer (at a cost of $200,000) who is effective at preparing the proposal in the best light. If neither hires a lawyer or if both hire lawyers, each side can expect to win about half the time. If only one side hires a lawyer, it can expect to win nine tenths, or 0.9, of the time. Use the given information to fill in the expected payoff, in dollars, for each cell in the matrix. (Hint: To find the expected payoff, multiply the probability of winning by the dollar amount of the payoff. Be sure to account for lawyer costs, which are incurred with certainty if a lawyer is hired.) Management (M) No Lawyer Lawyer No Lawyer L: $ , M: $ L: $ Labor (L) Lawyer L: $ M: $ L: $ The Nash equilibrium for this game is for Management to a lawyer, and for Labor to a lawyer. M: $ M: $

Every year, management and labor renegotiate a new employment contract by sending their proposals to an arbitrator, who chooses the best proposal (effectively giving one side or the other $5 million). Each side can choose to hire, or not hire, an expensive labor lawyer (at a cost of $200,000) who is effective at preparing the proposal in the best light. If neither hires a lawyer or if both hire lawyers, each side can expect to win about half the time. If only one side hires a lawyer, it can expect to win nine tenths, or 0.9, of the time. Use the given information to fill in the expected payoff, in dollars, for each cell in the matrix. (Hint: To find the expected payoff, multiply the probability of winning by the dollar amount of the payoff. Be sure to account for lawyer costs, which are incurred with certainty if a lawyer is hired.) Management (M) No Lawyer Lawyer No Lawyer L: $ , M: $ L: $ Labor (L) Lawyer L: $ M: $ L: $ The Nash equilibrium for this game is for Management to a lawyer, and for Labor to a lawyer. M: $ M: $

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.2: Guassian Elimination And Matrix Methods
Problem 87E
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5. Individual Problems 15-5 Every year, management and labor renegotiate a new employment contract by sending their proposals to an arbitrator, who chooses the best proposal (effectively giving one side or the other $5 million). Each side can choose to hire, or not hire, an expensive labor lawyer (at a cost of $200,000) who is effective at preparing the proposal in the best light. If neither hires a lawyer or if both hire lawyers, each side can expect to win about half the time. If only one side hires a lawyer, it can expect to win nine tenths, or 0.9, of the time. Use the given information to fill in the expected payoff, in dollars, for each cell in the matrix. (Hint: To find the expected payoff, multiply the probability of winning by the dollar amount of the payoff. Be sure to account for lawyer costs, which are incurred with certainty if a lawyer is hired.) Management (M) No Lawyer Lawyer No Lawyer L: $ M: $ L: $ Labor (L) Lawyer L: $ , M: $ L: $ The Nash equilibrium for this game is for Management to a lawyer, and for Labor to a lawyer. M: $ , M: s
Transcribed Image Text:5. Individual Problems 15-5 Every year, management and labor renegotiate a new employment contract by sending their proposals to an arbitrator, who chooses the best proposal (effectively giving one side or the other $5 million). Each side can choose to hire, or not hire, an expensive labor lawyer (at a cost of $200,000) who is effective at preparing the proposal in the best light. If neither hires a lawyer or if both hire lawyers, each side can expect to win about half the time. If only one side hires a lawyer, it can expect to win nine tenths, or 0.9, of the time. Use the given information to fill in the expected payoff, in dollars, for each cell in the matrix. (Hint: To find the expected payoff, multiply the probability of winning by the dollar amount of the payoff. Be sure to account for lawyer costs, which are incurred with certainty if a lawyer is hired.) Management (M) No Lawyer Lawyer No Lawyer L: $ M: $ L: $ Labor (L) Lawyer L: $ , M: $ L: $ The Nash equilibrium for this game is for Management to a lawyer, and for Labor to a lawyer. M: $ , M: s
1. Individual Problems 15-1 Mr. Ward and Mrs. Ward typically vote oppositely in elections, so their votes "cancel each other out." They each gain 16 units of utility from a vote for their positions (and lose 16 units of utility from a vote against their positions). However, the bother of actually voting costs each 8 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 minus sign if the payoff is negative.) Mrs. Ward Don't Vote Vote ,Mrs. Ward Vote Mr. Ward: Mr. Ward Mr. Ward: Mrs. Ward Don't Vote Mr. Ward: Mr. Ward: Mrs. Ward Mrs. Ward
Transcribed Image Text:1. Individual Problems 15-1 Mr. Ward and Mrs. Ward typically vote oppositely in elections, so their votes "cancel each other out." They each gain 16 units of utility from a vote for their positions (and lose 16 units of utility from a vote against their positions). However, the bother of actually voting costs each 8 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 minus sign if the payoff is negative.) Mrs. Ward Don't Vote Vote ,Mrs. Ward Vote Mr. Ward: Mr. Ward Mr. Ward: Mrs. Ward Don't Vote Mr. Ward: Mr. Ward: Mrs. Ward Mrs. Ward
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