Consider the following game. Alice and Bob simultaneously decide whether to watch hockey, basketball, and dancing. The payoff table is illustrated as follows, where the first number in each cell is Alice's payoff and the second is Bob's payoff.

Bob

hockey 2 basketball 2 dancing 2

hockey 1 1,1 0,2 0,3

Alice basketball 1 3,0 2,3 1,1

dancing 1 2,0 2,2 3,2

(a) List dominated strategies for both players. If there is none, write "none."

(b) List dominant strategies for both players. If there is none, write "none."

(c) Find all Nash equilibria