Adrian (player A) and Bani (player B) are in a restaurant. The owner offers 3 slices of pizza for free under the following condition. A and B announce the number of slices they would like. Each can announce (exactly) one of the four numbers: 5/22,S/2,S/2+2, and S. Let 3A and 33 respectively denote the numbers announced by A and B. If 3A + 53 g S, then each gets what they announce. Otherwise, if 3A + 83 > 3, each gets 0. We assume that player i's utility equals the number of slices player i gets. Both A and B maximize their own utility. Assume S = 8. (a) (1.5 points) Suppose A and B announce the number of slices simultaneously. In this simultaneous move game, the number of Nash equilibria in pure strategies ism (b) (1.5 points) Now consider a sequential move game where A proposes a split (3A, 5 3A) to B where, as before, 3A can take one of the four values: 3/272, 8/2,S/2 + 2, S. If B accepts the split, then A gets SA and B gets 3 SA- Else, if B rejects, each gets 0. If indifferent between accepting and rejecting a proposal, we assume B rejects