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PROBLEMS: CHAPTER 15 Problems: Chapter 15 Samantha Langevin Grand Canyon University: ECN-601 June 16, 2020 1
PROBLEMS: CHAPTER 15 15-1 To Vote or Not to Vote 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 lost two units of utility from a vote against their positions). However, the bother of actually voting cost each one unit of utility. Diagram a game in which they choose whether to vote or not. Mrs. Ward Vote Don’t Vote Mr. Ward Vote -1 , -1 1 , -2 Don’t Vote -2 , 1 0 , 0 The voting issue problem is a prisoners’ dilemma. The prisoners’ dilemma is a paradox in decision analysis in which two individuals acting in their own self-interest do not produce the optimal outcome (Chappelow, 2019). In this problem the above table depicts the conflict (self- interest) and cooperation of Mr. and Mrs. Ward and whether or not it is in their best interest to vote or to not vote. As you can see in the table above both Mr. and Mrs. Ward each have two options, to vote or not to vote. When both of them go to vote they, each get two units of utility from their vote and both of them also lose two units of utility because they typically vote oppositely. With that being said if both vote each of them loses one unit of utility as the cost of voting as shown above Mr. Ward -1 and Mrs. Ward -1. If Mrs. Ward votes and Mr. Ward does not than he loses two units of utility and Mrs. Ward gains one unit so Mr. Ward -2 and Mrs. Ward 1, and it would be vice versa if he were to vote and she did not, Mr. Ward 1 and Mrs. Ward -2. The one who did not vote would lose two units of utility because the other person voted for the person they would not have voted for and the one who voted wouldn’t have their vote canceled because of the others vote. Lastly, if neither of them was to vote they would neither gain nor lose 2
PROBLEMS: CHAPTER 15 anything because they chose not to vote, Mr. Ward 0 and Mrs. Ward 0. So, in this case the Nash equilibrium is for both Mr. and Mrs. Ward to vote since this is a prisoners’ dilemma and there is no way to tell if one will cheat and vote while the other does not.

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