Artemis and Diana are avid hunters. They devote Tuesdays to their shared hobby. On Monday evening, each of them separately writes, on a slip of paper, whether or not he or she will go hunting, and whether he or she wants to be the lead hunter, or the second hunter. They then meet and each reads what the other wrote.

If at least one of the two is not interested in going hunting, or both of them want the same role (lead hunter or second hunter), they do not go hunting on Tuesday.

If they are both interested in a hunt, one of them wants to be the lead hunter, and the other wants to be second hunter, they do go hunting on Tuesday. The utility of being lead hunter is 2. The utility of being second hunter is 1, and the utility of not going hunting is 0.

Answer the following questions for this situation of repeated interaction:

(a) Write down the base game for this situation.

(b) Find all the equilibria of the one-stage game (the base game).

(c) Find all the equilibria of the two-stage game.