You and a classmate had a conversation earlier in the day about meeting at the library to work on your problem set together. If either of you stay at home, you can work through it yourself but it will take longer. If you meet at the library you'll both get your problem sets done quickly. However, it's snowing outside so the worst outcome for either of you is walking all the way over there and having the other person not show up.

Suppose that consumer demand in an industry falls. Currently there are two firms operating in the industry. However, both of them realize that the industry will no longer be profitable with both firms in the market, and the only way to make money now is if the other firm exits.

You and your roommate share a small apartment.You're thinking about whether or not to invite your friends over tonight and your roommate is thinking about whether or not to invite hers.However, you don't really like your roommate's friends and she doesn't really like your friends. You would be very happy to have only your friends over, and very upset to only have hers. You would be slightly happy to have nobody over, and slightly upset if everyone shows up.Your roommate thinks the same way.

find the Nash equilibrium