Individual Problems $15-2$

Mr$.$ and Mrs$.$ Ward typically vote oppositely in elections and so their votes "cancel each other out." They each gain $14$ units of utility from a vote for their positions $($and lose $14$ units of utility from a vote against their positions$).$ However, the bother of actually voting costs each $7$ units of utility. The following matrix summarizes the strategies for both Mr$.$ Ward and Mrs$.$ Ward.

$\backslash$table$[[,$Mrs$.$ Ward,$],[$Mr$.$ Ward,Vote,Mr$.$ Ward: $-7,$ Mrs$.$ Ward: $-7,$Mr$.$ Ward: $7,$ Mrs$.$ Ward: $-14],[$Don$\text{'}$t Vote,Mr$.$ Ward: $-14,$ Mrs$.$ Ward: $7,$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 increase 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.