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. Suppose that each player enjoys $20 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 have cell phones, 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 equilibrium in pure strategies.
c) Which equilibrium would you consider to be a focal point?