Bruce, Colleen, and David are all getting together at
Bruce’s house on Friday evening to play their favorite game, Monopoly. They all
love to eat sushi while they play. They all know from previous experience that
two orders of sushi are just the right amount to satisfy their hunger. If they
wind up with less than two orders, they all end up going hungry and don’t enjoy
the evening. More than two orders would be a waste, because they can’t manage
to eat a third order and the extra sushi just goes bad. Their favorite
restaurant, Fishes in the Raw, packages its sushi in such large containers that
each individual person can feasibly purchase at most one order of sushi. Fishes
in the Raw offers takeout, but unfortunately doesn’t deliver.
Suppose that each player enjoys worth of utility from
having enough sushi to eat on Friday evening, and $0 from not having enough to
eat. The cost to each player of picking up an order of sushi is $10.
Unfortunately, the players have forgotten to communicate about who should be
buying sushi this Friday, and none of the players has a cell phone, so they
must each make independent decisions of whether to buy (B) or not buy (N) an
order of sushi.
(a) Write down this game in strategic form.
(b) Find all the Nash equilibria in pure strategies.
(c) Which equilibrium would you consider to be a focal
point? Explain your reasoning.