$80$ A new storefront has room for two new businesses. Elizabeth has rented out half of the space and is deciding whether to open a BBQ restaurant or a sandwich shop. Harper has rented out the other half of the space and is deciding whether to open a bakery $\frac{1}{d}$ or a plant shop. Each has done some market research and has determined how their profits will vary based on what stores are chosen. See the table below for more information.

$\backslash$table$[[,$Elizabeth's Ranking,Harper's Ranking$],[($Highest profit$),($BBQ$,$ Bakery$),($Sandwich$,$ Plant$)],[,($Sandwich$,$ Bakery$),($Sandwich$,$ Bakery$)],[,($Sandwich$,$ Plant$),($BBQ$,$ Plant$)],[($Lowest profit$),($BBQ$,$ Plant$),($BBQ$,$ Bakery$)]]$

So$,$ for example, Elizabeth's greatest profits come if she opens a BBQ restaurant and Harper opens a bakery, while Harper's greatest profits come if she opens a plant shop and Elizabeth opens a sandwich shop. Elizabeth and Harper cannot communicate, so this functions as a simultaneous game $($which is the only type of game we have discussed in class$).$ Which of the following is a Nash Equilibrium?

Hint: you should turn the above rankings into a payoff matrix and solve the payoff matrix like we did in class.

Elizabeth opens a sandwich shop, Harper opens a bakery

Elizabeth opens a sandwich shop, Harper opens a plant shop

This game does not have a Nash Equilibrium

Elizabeth opens a bakery, Harper opens a plant shop