Question 8 (3 points) 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: S/2 2, 5/2, 8/2 + 2, and S. Let 5;, and SB respectively denote the numbers announced by A and B. If 3,; + SB 3 S, then each gets what they announce. Otherwise, if SA + 53 > S, 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 = 6. (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 is E (b) {1 .5 points) Now consider a sequential move game where A proposes a split (3A, 3 SA) to B where, as before, SA can take one of the four values: Sf2 2, SIZ, Sf2 + 2, S. If B accepts the split, then A gets SA and B gets SSA. Else, if B rejects, each gets 0. If indifferent between accepting and rejecting a proposal, we assume B rejects. In the unique subgame perfect equilibrium of the game A proposes SA =D