Find the equilibria of the following two-player games, and describe what kind they are (Dominant Strategy, Iterated Elimination of Dominated Strategies, or Nash Equilibrium). Warning: Some games might not have a pure-strategy equilibrium!

1)

	Player 2
Player 1		Left	Middle	Right
Up	4 , 3	1, 5	1 , 4
Down	1 , 0	4, 1	2 , 2

2)

	Player 2
Player 1		Left	Right
Up	4 , 4	3 , 2
Down	2 , 3	0, 0

3)

	Player 2
Player 1		Left	Right
Up	1 , 4	3 , 2
Down	2 , 3	1 , 5

4)

	Player 2
Player 1		Left	Right
Up	1 , 3	4 , 2
Down	4 , 3	1 , 1

5)

	Player 2
Player 1		Left	Middle	Right
Up	1 , 4	5 , 1	3 , 2
Middle	2 , 3	6 , 1	2 , 2
	Down	1 , 3	3 , 2	4 , 5

6)

	Player 2
Player 1		Left	Middle	Right
Up	4 , 11	3 , 6	5 , 12
Middle	1 , 4	2 , 8	2 , 6
	Down	3 , 10	4 , 6	3 , 8

Now try this Three Player game. 7) Player 3 decides between Matrix 1 and Matrix 2.

Matrix 1	Player 2
Player 1		Left	Right
Up	1 , 4, 5	7 , 2, 4
Down	2 , 5, 2	0, 3, 6

Matrix 2	Player 2
Player 1		Left	Right
Up	2 , 1, 6	1 , 4, 5
Down	4 , 2, 4	3, 0, 3

8. Consider the Hotelling Location Game discussed in class. Suppose that a third business moves into town, trying to compete along the same one-mile road (perhaps it's another fellow with a hot dog cart). At first he moves to the middle of town, where the first two businesses are still standing, glaring at each other. These two fellows have split the town's customer base in half (due to transportation costs, as discussed in class). Should the third business locate in the middle, too? What happens if he, say, moves a bit to the west of the other two firms? Can you find a Nash Equilibrium?

9. Two coworkers annoy each other by wearing hideously ugly sweaters during the holidays. Suppose hi represents how hideous player i's sweater is (with 0 meaning "not at all ugly" and 5 meaning "unbearably ugly"), and player i's utility function is ,= 2. What is each player's best response function, and what are Nash Equilibrium levels of sweater hideousness? If the coworkers could both commit to not trolling each other with terrible sweaters (i.e. committing to hideousness of zero), would they be happier?