Wo entrepreneurs, Alice and Bill, are each deciding whether to open a restaurant that serves breakfast or a restaurant that serves dinner. Because there is limited demand for each type restaurant, the payoffs to each depend upon the type of restaurant the other opens, as shown in the following payoff matrix. Dinner

Alice

Breakfast

Bill

Dinner Breakfast

$1,000 for Alice

$1,000 for Bill

$1,600 for Alice

$1,400 for Bill

$1,400 for Alice

$1,600 for Bill

$800 for Alice

$800 for Bill

a. Suppose Alice and Bill make their decisions separately and simultaneously, so that each must decide what to do knowing the available choices and payoffs but not what the other has actually chosen. How many potential equilibria are there? (Hint: To see whether a given combination of strategies is an equilibrium, ask whether either player could get a higher payoff by changing his or her strategy.)

potential equilibria

b. Now suppose Alice makes her choice before Bill, and Bill can can see what kind of restaurant Alice opens before he makes his choice. What will be the equilibrium outcome?

multiple choice
They will both open a breakfast restaurant.
Alice will open a dinner restaurant, and Bill will open a breakfast restaurant.
Alice will open a breakfast restaurant, and Bill will open a dinner restaurant.
They will both open a dinner restaurant.