2. Individual Problems 15-2 Mr. and Mrs. Ward typically vote oppositely in elections and so their votes "cancel each other out." They each gain 24 units of utility from a vote for their positions (and lose 24 units of utility from a vote against their positions). However, the bother of actually voting costs each 12 units of utility. The following matrix summarizes the strategies for both Mr. Ward and Mrs. Ward. Mrs. Ward Vote Don't Vote Vote Mr. Ward: -12, Mrs. Ward: -12 Mr. Ward: 12, Mrs. Ward: -24 Mr. Ward Don't Vote Mr. Ward: -24, Mrs. Ward: 12 Mr. Ward: 0, Mrs. Ward: 0 The Nash equilibrium for this game is for Mr. Ward to and for Mrs. Ward to . Under this outcome, Mr. Ward receives a payoff of units of utility and Mrs. Ward receives a payoff of units of utility. Suppose Mr. and Mrs. Ward agreed not to vote in tomorrow's election. True or False: This agreement would decrease utility for each spouse, compared to the Nash equilibrium from the previous part of the question. O True O False This agreement not to vote a Nash equilibrium.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 10 units of utility from a 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 ut 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 Ward if they both vote. (Hint: Be sure to enter a minus sign if the payoff is negative.) Mrs. Ward Vote Don't Vote Vote Mr. Ward: Mrs. Ward Mr. Ward: Mrs. Ward Mr. Ward Don't Vote Mr. Ward: Mrs. Ward Mr. Ward: Mrs. Ward3. Individual Problems 15-3 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 6 units of utility, while the small rival suffers a loss of utility of 3. If the two companies select the same technology, Microsoft suffers a loss of utility of 3 while the rival gains 3 units of utility. Using the given information, fill in the payoffs for each celf in the matrix, assuming that each company chooses its technology simultaneously. Microsoft Technology A Technology B TechnologyA Rival: , Microsoftl Rival: I , Microsoft Rival _ _ Technology B Rival: , Microsoft Rival: , Microsoft True or False: There is no equilibrium in pure strategies. O True 0 False 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 $2 million). Each side can choose to hire, or not hire, an expensive labor lawyer (at a cost of $300,000) 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 four fifths, or 0.8, of the time. Use the given information to ll 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: I L: , M: Labor (L) Lawyer L: , M: L: . M: The Nash equilibrium for this game is for Management to V a lawyer, and for Labor to V a lawyer