Question

A. 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.

B. Suppose Mr. and Mrs. Ward agreed not to vote in tomorrow’s election. Would such an agreement improve utility? Would such an agreement be an equilibrium?

Answer 1

A. B.

Part I: If Mr. and Mrs. Ward agreed not to vote in tomorroew's election then such an agreement would improve utility because if both don't vote then the maximum payoff is (0,0) which is better than (-1,-1) which is if both decide to vote.

Part II: But the solution (0,0) is not an equilibrium. The above game is a Prisoner's Dilemma game and the Nash Equilibrium of this Vote-Not to Vote game is if both vote i.e, (-1,-1). This is because there is no surety that the other will not cheat and and vote. Hence, it is difficult to detect if one of them cheats and therefore difficult to maintain such an agreement.