Model the following situations as a game. Ensure that your game's payoffs match the situation. Your answer should consist of a payoff matrix, a short explanation, and an indication of the game's Nash equilibrium.

(i) You and your classmate plan to meet later at Subway to work on an assignment. If either of you stays home, you can work by yourself, but it will take longer to complete. If you both meet at Subway, you will both finish your problem sets more quickly. However, it is snowing outside, so the worst outcome for either of you is walking all the way there, and having the other person not show up.

(ii) Ben and Phil play rock-paper-scissors. The loser goes to the market to purchase dinner napkins, and the winner stays home. If they tie, they both go.

(iii) You and your roommate share a small apartment. You're considering inviting your friends over tonight, and your roommate is considering inviting hers. You hate your roommate's friends, and she hates yours. You would be very happy to have only your friends over, and very upset to have only hers. You would be slightly happy to have nobody over, and slightly upset if everyone shows up. Your roommate thinks the same way.