Consider a three player game between three players: Alice and Bob are roommates and they are planning to invite their neighbor Charlie to dinner. Alice comes home first and decides between cooking or watching a movie. Then, Bob comes home and observes Alices decision. If Alice is watching a movie (and has not cooked) Bob decides between cooking or watching the movie. Alice cooks seafood and vegetables, Bob cooks steaks for dinner. If there is food (either Alice or Bob cooks), they invite Charlie but not telling who cooked or whats for dinner. Charlie is a vegetarian, but Alice and Bob do not know about it. When Charlie receives the invitation he accepts or excuses himself (rejects). The payoffs are as follows:

If nobody cooks, there is no invitation and the game ends with each player getting a payoff of 1.

If Alice cooks and Charlie accepts, all are happy, each gets a payoff of 3.

If If Alice cooks and Charlie rejects all get 0.

If Bob cooks and Charlie accepts, Charlie gets 0 (no food for him) but Alice and Bob gets payoffs of 4 (more food for them).

If Bob cooks and Charlie rejects, Alice and Bob gets 0, Charlie gets 1.

(a) Draw the game tree and carefully label the information sets.

(b) Comment on each players best response to other two players strategies.

(c) Find the Nash equilibrium in this game?