Mr. and Mrs. Ward typically vote oppositely in elections and so their votes “cancel each other out.” They each gain 6 units of utility from a vote for their positions (and lose 6 units of utility from a vote against their positions). However, the bother of actually voting costs each 3 units of utility. The following matrix summarizes the strategies for both Mr. Ward and Mrs. Ward. Mrs. WardVoteDon't VoteMr. WardVoteMr. Ward: -3, Mrs. Ward: -3Mr. Ward: 3, Mrs. Ward: -6Don't VoteMr. Ward: -6, Mrs. Ward: 3Mr. 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.True False This agreement not to vote a Nash equilibrium.

The payoff matrix for the given game is Mrs. WardVote Don't VoteMr. WardVote -3,-33,-6Don't Vote -6,30,0A set of responses for the players where none has an incentive to change forms a Nash equilibrium. They do not deviate from their responses because that will reduce their payoff.The response of Mrs. Ward is will be,When Mr. Ward chooses Vote, Mrs. Ward will choose Vote as -3>-6.When Mr. Ward chooses Don't Vote, Mrs. Ward will choose Vote as 3>0.So the dominant strategy for Mrs. Ward is Vote.The response of Mr. Ward is will be,When Mrs. Ward chooses Vote, Mr. Ward will choose Vote as -3>-6.When Mrs. Ward chooses Don't Vote, Mr. Ward will choose Vote as 3>0.So the dominant strategy for Mr. Ward is Vote.The chosen strategies of the games is given in the following table. The green dots are the chosen strategies of Mr. Ward and the blue dots are of Mrs. Ward.When Mr. Ward chooses Vote then Mrs. Vote also chooses vote and when Mrs. Ward chooses Vote then Mr. ward also chooses Vote. So the response (Vote, Vote ) is the Nash Equilibrium of the game as neither of them has the incentive to move to other strategies.The Nash equilibrium for the game is for Mr. Ward to Vote and for Mrs.Ward to Vote. Under this outcome, Mr. Ward receives a payoff of -3 units of utility and Mrs. Ward receives a payoff of -3 units of utility.Mr. and Mrs. Ward agreed not to vote in tomorrow's election.When both choose not to vote then both will get a payoff of zero. Now 0>-3. So if both choose Don't Vote, then their payoff will increase.Therefore the given is False. This agreement between them is not a Nash Equilibrium as the Nash equilibrium is (Vote, Vote).(a)The Nash equilibrium for the game is for Mr. Ward to Vote and for Mrs. Ward to Vote. Under this outcome, Mr. Ward receives a payoff of -3 units of utility and Mrs. Ward receives a payoff of -3 units of utility.(b) The statement given is False as the payoff for (Don't Vote, Don't Vote) will increase both their utility.The not to vote agreement is not a Nash Equilibrium.

Answered: Mr. and Mrs. Ward typically vote…

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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Mr. and Mrs. Ward typically vote oppositely in elections and so their votes “cancel each other out.” They each gain 6 units of utility from a vote for their positions (and lose 6 units of utility from a vote against their positions). However, the bother of actually voting costs each 3 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: -3, Mrs. Ward: -3	Mr. Ward: 3, Mrs. Ward: -6
Don't Vote	Mr. Ward: -6, Mrs. Ward: 3	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.

True

False

This agreement not to vote a Nash equilibrium.

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