CONTEXT: Roxanne, Sara, and Ted all love to eat cookies, but there is only one left in the package. No one wants to split the cookie, so Sara proposes the following method of allocating the cookie to one of them. On the count of three, each of them will show one or two fingers, they will add them up, and then divide the sum by 3. If the remainder is 0, then Roxanne gets the cookie. If the remainder is 1, Sara gets it. If the remainder is 2, Ted gets it. Each of them receives a payoff of 1 for winning and 0 otherwise.

QUESTION 1: What are the Nash equilibria of the game described in Question 16? Select all that apply.

1. (2, 1, 1)
2. (1, 2, 1)
3. (2, 1, 2)
4. (2, 2, 1)
5. (1, 2, 2)
6. (1, 1, 1)
7. (2, 2, 2)
8. (1, 1, 2)

QUESTION 2:

Is the game from Question 16 a fair mechanism for allocating cookies?