1 . Individual Problems 15-2

Mr. and Mrs. Ward typically vote oppositely in elections and so their votes "cancel each other out." They each gain 26 units of utility from a vote for their positions (and lose 26 units of utility from a vote against their positions). However, the bother of actually voting costs each 13 units of utility. The following matrix summarizes the strategies for both Mr. Ward and Mrs. Ward.

Mrs. Ward

Vote

Don't Vote

Mr. Ward

Vote

Mr. Ward: -13,Mrs. Ward: -13

Mr. Ward: 13,Mrs. Ward: -26

Don't Vote

Mr. Ward: -26,Mrs. Ward: 13

Mr. Ward: 0,Mrs. Ward: 0

he Nash equilibrium for this game is for Mr. Ward to(vote or not vote)and for Mrs. Ward to(vote or not vote). 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 increase utility for each spouse, compared to the Nash equilibrium from the previous part of the question.

This agreement not to vote(is or is not)a Nash equilibrium.

2 . 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 4 units of utility, while the small rival suffers alossof utility of 2. If the two companies select the same technology, Microsoft suffers alossof 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 ATechnology B

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.