Question

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.

Answer 1

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 the both vote.(Be sure to enter a minus sign if the payoff is negative).

Both Mr. Ward and Mrs. Ward each have two options : Vote or Don't Vote.

If Mr. Ward votes then the possible payoffs are determined by the strategy that Mrs. Ward chooses. If she also chooses to vote both will get a payoff of 4 units of utility, but since each also vote for the opposition both also loose 4 units of utility. Furthermore, both incur the cost of voting, equal to 2 units of utility.Therefore,the payoff for both in this situation is 4 - 4 - 2 = -2.

Now assume that Mr. Ward votes, if Mrs. Ward chooses not to vote, then she will get a payoff of -4 unit of utiity,Mr. Ward will get 4 unit of utility from voting and incurred the 2 unit of cost of voting, but has not had his vote cancelled out. Therefore , Mr. Ward will get payoff for this is 4 - 2 = 2